Mathematics is an important subject which students generally find tough to crack. But with regular practice and reading, students can master the subject. Read this article to learn how to calculate square root of 2.
Square root definition can be defined as a number which when multiplied by itself gives a as the product, then it is known as a square root. For example, since
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 Returning the Square root of 2 value (SQRT2)
 Returning the square root value of 4 (sqrt4)
 Returning the square root values for different numbers
 Returning the square root value of ‘36’
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 LaTeX square root Example
 1. Velocity from position vector in LaTeX
 2. Root of quadratic equation
 3. Momentum from Kinetic energy
 4. Spacetime equation
 Square Root Symbol
 How to Calculate the Value of a Square Root of 10?
 What is the Square Root of 10?
 What is a Square Root?
 How to Find the Square Root of a Number?
 Tricks to Calculate Square Root
 Square Root Trick for 4 Digit Numbers
 Square Root Table From 1 to 50
 Using a Long Division Algorithm
 Understanding the Process
 Square Root Table
 How To Find Square Root?
 General Root Calculator
 Estimating a Root
 Estimating an nth Root
 Root 2 Value Calculation
 How To Find Root 2 Value?
 Value of Square Root of 2 by Long Division Method
 Sample Question on Square Root of 2
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 Square Root Values
When two equal numbers are multiplied, it results in a perfect square. For example,
This is a basic property of the square root
Value of root 3+2 root 2?
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Value of root 3+2 root 2?
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LCM of root 2 and root 3 is?
LCM of root 2 and root 3 is?
**Finding the LCM of √2 and √3**
To find the least common multiple (LCM) of √2 and √3, we need to understand what LCM means and how it can be calculated.
**What is LCM?**
The least common multiple (LCM) of two or more numbers is the smallest multiple that is divisible by each of the given numbers. In other words, it is the smallest number that all the given numbers can divide evenly into.
There are various methods to find the LCM of numbers, including prime factorization method, listing multiples, and using the LCM formula. Let’s use the prime factorization method to find the LCM of √2 and √3.
**Prime Factorization Method**
1. Start by expressing each number as a product of its prime factors.
√2 = √(2 × 1) = √2
√3 = √(3 × 1) = √3
It is important to note that both √2 and √3 are already in their simplest radical form.
2. Identify the common and uncommon prime factors.
In this case, there are no common prime factors between √2 and √3.
3. Multiply the common and uncommon prime factors.
Since there are no common prime factors, we multiply the individual prime factors.
√2 × √3 = √(2 × 3) = √6
Therefore, the LCM of √2 and √3 is √6.
The LCM of √2 and √3 is √6 because √6 is the smallest number that both √2 and √3 can divide evenly into.
To further confirm this, we can check whether √6 is divisible by both √2 and √3.
√6 ÷ √2 = √(6 ÷ 2) = √3
√6 ÷ √3 = √(6 ÷ 3) = √2
Since both divisions result in perfect square roots, we can conclude that √6 is divisible by both √2 and √3.
Hence, the LCM of √2 and √3 is √6.
which is actually the content of /etc/environment
For root I get:
what’s the reason behind this and which file contains this line?
asked Nov 20, 2012 at 9:08
PATH is an environment variable, and therefor it ‘defaults’ or ‘resets’ when you change environment. See man sudoers
for an explanation:
env_reset If set, sudo will reset the environment to only contain
the LOGNAME, SHELL, USER, USERNAME and the SUDO_* vari
ables. Any variables in the caller's environment that
match the env_keep and env_check lists are then added.
The default contents of the env_keep and env_check
lists are displayed when sudo is run by root with the
V option. If sudo was compiled with the SECURE_PATH
option, its value will be used for the PATH environment
variable. This flag is on by default.
The wiki has some more information (amongst others which files are used to add to PATH): https://help.ubuntu.com/community/EnvironmentVariables
answered Nov 20, 2012 at 9:31
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You can check any of those files (these are the common ones i know of) for lines such as
export PATH=$PATH:/usr/games:/usr/local/games:/home/monty/google_appengine
or
export PATH=/usr/lib/lightdm/lightdm:$PATH
Edit
.bashrc
and .profile
seem to have default versions(/etc/profile/
and /etc/bash.basrhc
) in /etc/
you can check them for the path for Root.
answered Nov 20, 2012 at 9:28
Karthik T
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How to return the square root value in JavaScript?
The square root of a number is a value that, when multiplied by itself, gives the number.
In JavaScript, by using SQRT
property & sqrt()
Method we can return the square root value.
Difference between SQRT & sqrt
SQRT
sqrt()
are used to find the value of square root in JavaScript.SQRT
is a property, where assqrt()
is a method.SQRT
SQRT2
SQRT1_2
sqrt()
method has no parameters, that means we can enter the input value manully insqrt()
Eg:sqrt(36)
SQRT
property returns only the square root values of . Where assqrt()
method returns square roots for all the input numbers, except the negative numbers.
Returning the square root values by using SQRT
EXAMPLE: Returning the Square root of 1/2 value (SQRT1_2
).
<p>Click the below button to return Square root.</p> <input type="button" onclick="" value="Click"> <p id=""></p> <script> function { document.getElementById("").innerHTML = Math; } </script>
Returning the Square root of 2 value (SQRT2
)
<p>Click the below button to return Square root.</p> <input type="button" onclick="" value="Click"> <p id=""></p> <script> function { document.getElementById("").innerHTML = Math; } </script>
Square root of 2
Returning the values of square root by using sqrt
property.
Returning the square root value of 4 (sqrt4
)
<p>Click the below button to return Square root.</p> <input type="button" onclick="" value="Click"> <p id=""></p> <script> function { document.getElementById("").innerHTML = ; } </script>
Square root of 4
Returning the square root values for different numbers
<p>Click the below button to return Square root.</p> <input type="button" onclick="" value="Click"> <p id=""></p> <script> function { var a = ; var b = ; var c = ; var d = ; var e = ; var f = ; var g = ; var h = ; var r = a + "<br>" + b + "<br>" + c + "<br>" + d + "<br>" + e + "<br>" + f + "<br>" + g + "<br>" + h; document.getElementById("").innerHTML = r; } </script>
Square roots of different values
NOTE: The sqrt()
method returns output » for the negative input numbers.
Returning the square root value of ‘36’
<p>Click the below button to return Square root.</p> <input type="button" onclick="" value="Click"> <p id=""></p> <script> function { document.getElementById("").innerHTML = ; } </script>
Square root of nageative value
In the above code snippet we have given negative value to the sqrt()
method. The sqrt()
method returns » as output to the negative numbers.
To create persistent environment variables, I add the script file to /etc/profile.d directory, for example:
# my script export MY_VAR=var_value
alex@alex64:~$ echo $MY_VAR var_value
alex@alex64:~$ echo $MY_VAR var_value alex@alex64:~$ sudo su root@alex64:/home/alex# echo $MY_VAR root@alex64:/home/alex#
How can I set the same variables for the root?
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asked Jul 10, 2012 at 10:30
sudo does not normally preserve local environment variables. You should use it with the E
switch to do so, i.e. sudo E su
will preserve $MYVAR for root.
Alternatively, to create persistent variables that are truly systemwide, you should set them in /etc/environment
.
answered Jul 10, 2012 at 10:47
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Defaults env_reset
in /etc/sudoers
will reset root’s PATH
defined by /etc/environment
.
You could modify it to Defaults !env_reset
to disable resetting or add:
Defaults secure_path="my/custom/path:/bin:/usr/bin:/usr/local/bin:/sbin:/usr/sbin
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answered Nov 27, 2013 at 14:14
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Like the process you define your own environment variable, for example by editing ‘~/.bashrc’, you can define root’s environment variable by editing ‘/root/.bashrc’.
answered May 21, 2015 at 14:50
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You can pass environment variables using env
flag. I always need to get around proxies and this is a constant issue for me. Especially when you need to pass PATH
and proxy environment variables.
sudo env "ENV=$ENV1" "ENV2=$ENV2" [command]
And you can add it as an alias (add this .bashrc
, .bash_aliases
or .zshrc
etc).
Example of my alias:
alias psudo='sudo env "PATH=$PATH" "HTTP_PROXY=$HTTP_PROXY" "HTTPS_PROXY=$HTTPS_PROXY" "http_proxy=$http_proxy" "https_proxy=$http_proxy"'
Be mindful that this obviously reduces the security of sudo.
answered Oct 28, 2020 at 4:47
Emmanuel N KEmmanuel N K
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What is the value of root 3 by 4?
Introduction:
Root 3 by 4 is a mathematical term that represents a fractional value that involves a square root of 3 and a denominator of 4. This value is commonly used in trigonometry and geometry to calculate various measurements and angles.
Finding the Value:
To find the value of root 3 by 4, we need to simplify the expression by rationalizing the denominator. We do this by multiplying both the numerator and denominator by the conjugate of the denominator, which is also root 3 plus 4.
Simplification:
Multiplying the numerator and denominator by root 3 plus 4, we get:
(root 3 / 4) x (root 3 + 4) / (root 3 + 4)
= (root 3 x root 3 + root 3 x 4) / (4 x (root 3 + 4))
= (3 root 3 + 4 root 3) / (4 root 3 + 16)
= 7 root 3 / (4 root 3 + 16)
Final Answer:
This expression cannot be simplified further, so the value of root 3 by 4 is 7 root 3 / (4 root 3 + 16).
What is the value of root 3 by 4?
0.433 is answer
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With the help of Latex, when the root symbol is used in a science document, you need to call the \sqrt
command.
And you have to pass two arguments in this \sqrt
command, one is the value of the root and the other is the expression. Notice this syntax below
However, there is no need to add root value with \sqrt
command in case of square root. Then, the syntax of the command will be
For example, if we want to define the square root of x with the help of latex, then x has to be passed to the \sqrt
command as an expression and there is no need to give the value of the root.
\documentclass{article}
\begin{document}
$\sqrt{x}$
\end{document}
And if you use nth root instead of square root then you have to pass n as the value of root.
\documentclass{article}
\begin{document}
$\sqrt[n]{x}$
\end{document}
LaTeX square root Example
Below we will discuss some important concepts that you are familiar with. Because when you create a science document with latex, this concept will be useful in most cases.
1. Velocity from position vector in LaTeX
Here the value of velocity has to be determined using square root
\documentclass{article}
\begin{document}
$v=\sqrt{\left ( \frac{dx}{dt} \right )^{2}+\left ( \frac{dy}{dt} \right )^{2}+
\left ( \frac{dz}{dt} \right )^{2}}$
\end{document}
Looking at the output above, you can see that the size of the square root symbol will decrease and increase dynamically according to the size of the expression.
2. Root of quadratic equation
You all know how to write the root of quadratic equation! Suppose, if the quadratic equation is ax²+bx+c, then root will be
\documentclass{article}
\begin{document}
$\frac{b \pm \sqrt{b^24ac}}{2a}$
\end{document}
3. Momentum from Kinetic energy
You also need to use the square root symbol when determining the momentum from kinetic energy.
\documentclass{article}
\begin{document}
$p=\sqrt{2mK}$
\end{document}
4. Spacetime equation
You all know that the Theory of Relativity has been given an important equation over time
\documentclass{article}
\begin{document}
$t'=\frac{t}{\sqrt{1\frac{v^2}{c^2}}}$
\end{document}
Notice that the Latex command will always return a square root symbol with dynamic size. And with this command, you just have to pass the expression.
Square root is the most significant topic in Mathematics. It is widely used by the students to resolve the questions based on square roots. The concept of Square root was found many years ago. The history of the square root originated throughout the world from Ancient Greece to Ancient India. In this article, we will discuss the concepts of square root, Square root symbol and how to derive or calculate the square root of 10 values or root 10 values.
The square root of 10 or root 10 value is 3.162
The square root of any number gives the same number when the number multiplied by itself.
Square Root Symbol
The symbol used to denote the square root is «√». It is also known as a radical symbol or radix. The number written under the square root symbol is called the radicand. The square value can be represented in the radical form as well as in decimal form. Square root of 10 can also be represented as a radical of 10.
How to Calculate the Value of a Square Root of 10?
Calculating the root 10 value is a bit complex because the number 10 is not a perfect square as its unit digit is 0. Square root of a number can be easily obtained if the number is in a perfect square. The number is considered as a perfect square if it can be denoted as a product of two equal integers.
For example 5×5= 25, it is representing the square of a number 5. It is considered as a perfect square as it is stated as a product of two similar integers i.e. 5 x 5 = 25, 6 x 6= 36. It is representing the square of 6. It is even considered as a perfect square as it is stated as a product of two similar integers i.e. 6 x 6.
The number is a perfect square if the unit place of a number ends with 1,4,5,6 or 9
The number is not said to be a perfect square if it ends with 2, 3, 7 or 8.
We can calculate the value of a square root or root 10 values through two methods.
First method to calculate the value of a square root or root 10 value is to use the unit digit of the given number,
The second method to calculate the square root value or root 10 values of the given number is by using a long division method.
What is the Square Root of 10?
The square root of 10 or root 10 is represented in the form of √10. As we know 10 is an even number but not a prime number. Prime numbers are considered as those numbers which have only two factors i.e. 1 and the number itself. For example 2 is a prime number as it has only factors 1 and 2 itself. But number 10 is not a prime number because it has multiple factors like.
1×10 = 10
2 x 5= 10
10 x 1 = 10
5 x 2 = 10
To calculate the square root of value 10, write its factors first
10 = 2 x 5
Square root of 10 can be written in the below format
Common square terms out of the root in the above equation cannot be taken out as it has no common square terms.
Hence, the value of root 10 or root 10 is 3.162
Square root of 10 using Long Division Method
(division method image will be uploaded soon)
Are you taking extra time than it actually requires to solve complex square root equations? Well, now with the help of square root tricks you can find the square of numbers very easily and with much less time. Square roots are very important from an examination point of view as it is needed in almost every topic. Tips and tricks always help us to solve mathematical problems easily and swiftly. Therefore, we have here for you a few helpful tips with which you can find the square root of a given number without any kind of help, especially that of a calculator. Without knowing these tips and tricks, it can be timeconsuming to find a simple square root of a number.
To begin with, finding the square root of a number, what we have to know first is if the number is a perfect square or not. And we all know that there are two conditions to find if a number is a perfect square or not. First, a number will be a perfect square if it ends with 1, 4, 5, 6, and 9. Second, a number will never be a perfect square if it ends with 2, 3, 7, and 8. These two tips are the most basic tips to find square roots but they are not enough.
(Image will be uploaded soon)
What is a Square Root?
The square root of a number is a value that we get when it is multiplied by itself and produces the original number. For example, when 5 is multiplied by itself we get 25. Thus we can say that 5 is a square root value of 25. In the same way, 4 is the square root value of 16, 6 is the square root value of 36, and 7 is the square root value of 49.
Now, just like a square is a representation of the area of a square that is equal to the side x side, the square root is the representation of the length of the side of a square.
The square root of a number can be rational or irrational. If the square root of a number is an integer, it is a perfect square.
How to Find the Square Root of a Number?
Finding the square root of numbers such as 4, 9, 16, 25, etc. is quite easy, and I’ll tell you why. It is because we all know that from the multiplication table of 1 to 10, the number which is multiplied by itself gives the squares in a twodigit form. But what if a number is in threedigits or fourdigits? Well, then it is considered difficult to find the root of these numbers. And that is because we fail to remember the table for higher numbers. So why not know the trick behind to determine the root of larger numbers?
Tricks to Calculate Square Root
You can use the trick to estimate the square root of the perfect square number. To find the square root without long division, you need to know the square root of the first 10 numbers. The square roots of the first 10 numbers are
Square Root Trick for 4 Digit Numbers
Pair the numbers from the right hand side.
Compare the unit digits of the numbers in the figure to determine the possible values for the square root of the unit digits.
Let’s take a look at the first pair of numbers. Let’s say «n».
Determine the two squares where this number is between √a < n < √b, then a < n < b. Therefore, the tens digit of square roots of the required is «a».
As shown in the square table, there are only two numbers and the square does not repeat which is 5 or 10. Confirm that the unit number obtained in step 2 is one of them.
Multiply a and b.
Select b if ab ≤ n, otherwise select a.
Let us consider that we need to find the square root of a large number of 4489.
Here, in this number, the unit digit is 9 that means it can be a unit digit of its square root number that is 3 or 7 that is because 32 is 9 & 72 is 49.
Now if we consider the first two digits, that is 44, it comes between the squares of 6 and 7 because 62 < 44 < 72.
We can expect that in the ten’s digit of the square root of 4489,the lowest amidst the two numbers is 6 and we want to find the unit digit of the square root of the number 4489.
Now, we would want to find if 63 or 67 is the square root of 4489.
Considering the ten’s digit is 6 and the next number is 7, we have to multiply both the numbers like 6 x 7 = 42 and because 42 is less than 44.
Square root of 4489 has to be the bigger number between 63 and 67 i.e. 67.
We can have a look at one more example, the square root of 7056.
Given below is the step by step method:
Now, in this number, the unit digit is 6. All the numbers which have the unit digit as 6 on their square roots. are 4 and 6.
Now consider that the first two digits i.e., 70 come between the squares of 8 and 9 because of 82 < 70 < 92.
Assume that in the ten’s digit of the square root of the 7056, the lowest amidst the two numbers is 8.
So, we have to find the unit digit of the square root of the number 7056. And for that, we have to find between 84 and 86 which one is the square root of 7056.
Since the ten’s digit is 8 and the proceeding number is 9, we have to perform multiplication of both the numbers like 8 x 9 = 72 and because 72 is greater than 70.
The square root of 7056 needs to be a lesser number between 84 and 86 that is 84.
There are various square roots tricks pdfs which contain more tricks just like this method that you can find on the web. Try to find the square roots of large numbers using these tricks, and you will be able to solve an equation within no time.
Given below is a table of square roots from numbers 1 to 50. This table will help you to solve the problems based on them very easily.
Square Root Table From 1 to 50
In the days before calculators, students and professors alike had to calculate square roots by hand. Several different methods have evolved for tackling this daunting process, some giving a rough approximation, others giving an exact value. To learn how to find a number’s square root using only simple operations, please see Step 1 below to get started.
Using a Long Division Algorithm
Understanding the Process

Consider the number you are calculating the square root of as the area S of a square. Because a square’s area is L^{2} where L is the length of one of its sides, therefore, by trying to find the square root of your number, you are trying to calculate the length L of the side of that square.

Specify letter variables for each digit of your answer. Assign the variable A as the first digit of L (the square root we are trying to calculate). B will be its second digit, C its third, and so on.

Specify letter variables for each «chunk» of your starting number. Assign the variable S_{a}to the first pair of digits in S (your starting value), S_{b} the second pair of digits, etc.

Understand this method’s connection to long division. This method of finding a square root is essentially a long division problem that divides your starting number by its square root, thus giving its square root as an answer. Just like in a long division problem, in which you are only interested by the next one digit at a time, here, you are interested by the next two digits at a time (which correspond to the next digit at a time for the square root).

Find the biggest number whose square is less than or equal to S_{a}. The first digit A in our answer is then the biggest integer where the square does not exceed S_{a} (meaning A so that A² ≤ Sa < (A+1)²). In our example, S_{a} = 7, and 2² ≤ 7 < 3², so A = 2.
 Note that, for instance, if you wanted to divide 88962 by 7 via long division, the first step would be similar: you would be looking at the first digit of 88962 (8) and you would want the biggest digit that, when multiplied by 7, is lower than or equal to 8. Essentially, you’re finding d so that 7×d ≤ 8 < 7×(d+1). In this case, d would be equal to 1.

Visualize the square whose area you are beginning to solve. Your answer, the square root of your starting number, is L, which describes the length of a square with area S (your starting number). Your values for A,B,C, represent the digits in the value L. Another way of saying this is that, for a twodigit answer, 10A + B = L, while for a threedigit answer, 100A +10B + C = L, and so on.
 In our example, (10A+B)² = L^{2} = S = 100A² + 2×10A×B + B². Remember that 10A+B represents our answer L with B in the units position and A in the tens position. For instance, with A=1 and B=2, 10A+B is simply the number 12. (10A+B)² is the area of the whole square, while 100A² the area of the biggest square inside, B² is the area of the smallest square, and 10A×B is the area of each of the two remaining rectangles. By performing this long, convoluted process, we find the area of the entire square by adding up the areas of the squares and rectangles inside it.

Subtract A² from S_{a}. Drop one pair (S_{b}) of digits from S. S_{a} S_{b} is nearly the total area of the square, which you just subtracted the area of the bigger internal square from. The remainder is can be though of as the number N1, which we obtained in step 4 (N1 =380 in our example). N1 is equal to 2×10A×B + B² (area of the two rectangles plus area of the small square).

Look for N1 = 2×10A×B + B², also written as N1 = (2×10A + B) × B. In our example, you already know N1 (380) and A (2), so you need to find B. B is most likely not going to be an integer, so you must actually find the biggest integer B so that (2×10A + B) × B ≤ N1. So, you have: N1 < (2×10A + (B+1)) × (B+1).)

Solve. To solve this equation, multiply A by 2, shift it in the position of the tens (which is equivalent to multiplying by 10), place B in the position of the units, and multiply the resulting number by B. In other words, solve (2×10A + B) × B. This is exactly what you do when you write «N_×_=» (with N=2×A) in the bottom right quadrant in step 4. In step 5, you find the biggest integer B that fits on the underscore so that (2×10A + B) × B ≤ N1.

Subtract the area (2×10A + B) × B from the total area. This gives you the area S(10A+B)² not yet accounted for (and which will be used to calculate the next digits in a similar fashion).

Add New Question
Is 28 a perfect number?
Yes. A «perfect» number is a positive integer which is the sum of all of its positive divisors (except itself). Thus, 28 = 1 + 2 + 4 + 7 + 14.
What is the square root of 0.000121?
.011. If you are calculating it by hand, here’s what to do: 121’s sqrt is 11. To get .000121, you simply find an amount of 0’s after the decimal point and the number 11 afterwards. Then multiply by itself. .011*.011= .000121.
Can I write the cube root of x as (1/x)^1/3?
No, it’s (x)^1/3.
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This method works for any base, not just in base 10 (decimal).
In the example, 1.73 can be considered to be a «remainder» : 780.14 = 27.9² + 1.73.
Moving the decimal point by an increment of two digits in a number (factor of 100), moves the decimal point by increments of one digit in its square root (factor of 10).
Show More Tips
Be sure to separate the digits into pairs from the decimal point. Separating 79,520,789,182.47897 as «79 52 07 89 18 2.4 78 97″ will yield a useless number.
Square Root Table
Referring to this square root table, half of the energy will be saved.
How To Find Square Root?
Now, since we know what a square root is, we can quickly jump into knowing how to find a square root of a number. There is no square root formula as such but well, there are two ways to find the square root of a number. They are the Prime Factorization Method and the Division Method. You will know how to solve the square root equation using these two methods.
Finding Square Root Using Prime Factorization Method
First resolve the given number into prime factors.
Make pairs of similar factors.
The product of prime factors, chosen one out of every pair, gives the square root of the given number.
find the square root of 24336.
Resolving 24336 into prime factors, we get:
Finding Square Root Using Division Method
Mark off the digits in pairs starting with the unit digit. Every pair and remaining one digit (if any) is called a period.
Think of the largest number whose square is equal to or just less than the first period. Take this number as the divisor as well as quotient.
In this step subtract the product of divisor and quotient from the first period and bring down the next period to the right of the remainder. This becomes the new dividend.
now, a new divisor is obtained by taking twice the quotient and annexing with it a suitable digit which is also taken as the next digit of the quotient, chosen in such a way that the product of new divisor and this digit is equal to or just less than the new dividend.
Question 1) By using the table of square roots, find the values of
x = 13
x = 83
Question 2) find the square root of 1764
Resolving 1764 into prime factors, we get:
Question 3) Find the smallest number which when multiplied by 720 gives a perfect square number.
i) Give the perfect square number so obtained?
ii) Find the square root of this perfect square number.
Resolving 720 into prime factors, we get:
720 = 2 × 2 × 2 × 2 × 3 × 3 × 5.
Thus, 2,2,3 exist in pairs while 5 is alone.
So, we should multiply the given number by 5 to get a perfect square number.
i) Perfect square number so obtained = 720 × 8 = 3600
ii) Now, 3600 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5
General Root Calculator
In mathematics, the general root, or the n^{th} root of a number a is another number b that when multiplied by itself n times, equals a. In equation format:
^{n}√ = b
b^{n} = a
Estimating a Root
Some common roots include the square root, where n = 2, and the cubed root, where n = 3. Calculating square roots and n^{th} roots is fairly intensive. It requires estimation and trial and error. There exist more precise and efficient ways to calculate square roots, but below is a method that does not require a significant understanding of more complicated math concepts. To calculate √:
 Estimate a number b
 Divide a by b. If the number c returned is precise to the desired decimal place, stop.
 Average b and c and use the result as a new guess
 Repeat step two
Estimating an n^{th} Root
 Estimate a number b
 Divide a by b^{n1}. If the number c returned is precise to the desired decimal place, stop.
 Average: [b × (n1) + c] / n
 Repeat step two
It should then be clear that computing any further will result in a number that would round to 1.403, making 1.403 the final estimate to 3 decimal places.
Root 2 Value Calculation
Any root value when multiplied by itself gives the number that is under the root symbol. For example, √5 x √5 = 5 or √44 x √44 = 44, similarly, √2 x √2 = 2. Some important points on the square root are given below:
 i) A square root of a number n is a number m which, when multiplied by itself, equals n.
 ii) The square roots of 36 are 6 and – 6 because 6^{2} = 36 and (– 6)^{2} = 36.
 iii) If m^{2} = n, then m is a square root of n.
Value of root 2 up to 50 decimal places
How To Find Root 2 Value?
Students can easily find the value of sqrt of a number if that number is a perfect square. Example: The value of √4 is 2 as 4 is a perfect square of 2, and the value of √625 is 25 as 25 x 25 = 625. So, finding √ of a perfect square is easy.
The challenge is to find the square root of not perfect square numbers. For numbers that are not a perfect square, we use the long division method.
Value of Square Root of 2 by Long Division Method
The long division method is the universal way to find out the root of any number irrespective of its type. Through this section we will explain the long division method in step by step:
 1st Step: Put a bar over e Put a bar over each pair of digits starting from one’s place. If the number of digits in it is odd, then the leftmost digit too will have a bar.
 2nd Step: Check the largest number whose square is ≥ the number under the extreme left bar. Take the no. as the new divisor and the quotient with the number that is under the extreme left as the dividend and Divide to get the next remainder.
 3rd Step: Bring down the number under the next bar to the right of the remainder.
 4th Step: Double the quotient and enter it with a blank on its right.
 5th Step: Repeat steps 2, 3, 4 till the remainder is 0 or is repetitive.
 6th Step: The quotient will be the square root value.
Sample Question on Square Root of 2
Here are some questions that will aid students in their preparation:
Q.1: What is the value of the square root of 2?
Ans: Square root 2 equals 1.414.
Q.2: How to calculate square root value using the long division method?
Q.3: Why is √ 2 an irrational number?
Ans: Since √ 2 is not an integer, when we find the value of √ 2 the numbers after the decimal point tend to infinity, it is irrational.
Q.4: What is the value of one divided by root 2?
Ans: The value of one by root 2 is 0.707.
Q.5: Can a number have 2 square roots?
Ans: Every number except 0 has two square roots, a positive and a negative.
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About This Article
To calculate a square root by hand, first estimate the answer by finding the 2 perfect square roots that the number is between. A perfect square root is any square root that’s a whole number. For example, if you’re trying to find the square root of 7, first you’d need to find the first perfect square below 7, which is 4, and the first perfect square above 7, which is 9. Then, find the square root of each perfect square. The square root of 4 is 2, and the square root of 9 is 3. Therefore, you know that the square root of 7 falls somewhere between 2 and 3. Now, divide your number by one of the perfect square roots you found. For example, you would divide 7 by either 2 or 3. If you were to choose 3, your answer would be 2.33. Next, find the average of that number and the perfect square root. To find the average in this example, add 2.33 and 2, then divide by 2 and get 2.16. Repeat the process using the average you got. First, divide the number you’re trying to find the square root of by the average. Then, find the average of that number and the original average by adding them together and dividing by 2. For example, first you would divide 7, the number you started with, by 2.16, the average you calculated, and get 3.24. Then, you’d add 3.24 to 2.16, the old average, and divide by 2 to find the new average, which is 2.7. Now, multiply your answer by itself to see how close it is to the square root of the number you started with. In this example, 2.7 multiplied by itself is equal to 7.29, which is 0.29 away from 7. To get closer to 7, you would just repeat the process. Keep dividing the number you started with by the average of that number and the perfect square, using that number and the old average to find the new average, and multiplying the new average by itself until it equals your starting number. If you want to learn how to use the long division algorithm to find the square root, keep reading the article!
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Square Root Values
1. Find the value of √80 + 16√5 , if 3√5+√125 = 17.88
= 3√5 + √125 = 17.88
= 3√5 + (√25 x √5) = 17.88
= 3√5 + 5√5 = 17.88
= 8√5 = 17.88
= √5 = 17.88/8
= √80 + 16√5 = √16 x √5 + 16 √5
= 4√5 + 16√5 = 20√5
= 20 x 17.88/8 = 44.7
2. Simplify: (√7 1/√7)
= (√7 1/√7)
= (√7 1/√7)
– 2 x √7 x 1√7 + (1/√7)
= 5 + 1/7
The Yale Babylonian has a tablet from nearly 4000 years ago that states the square root of 2 out to 9 decimal places by making use of a square and two diagonals.
Communities in Ancient India were making use of square roots since 800 BCE.
An Indian Mathematician from the 9 century named Mahavira is the first person to announce that negative square roots do not take place.
Procedure to determine the square root is outlined in the Chinese book, Writings on Reckoning, written in around 200 BCE during the Han Dynasty.
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