Square Root of 1156

Square Root of 1296

The square root of 1296 is also called root 1296 in short form. The square root of a number can be a rational/irrational number, positive/negative number, real/imaginary number. 1296 is a special number with its square root being a perfect square. Now we will see some cool facts about the square root of 1296 and few interesting problems as well.

Square Root of 1156

Squaring and finding the square root are inverse operations. When 1156 = a number × a number,  then  √1156 = a number.  In this lesson, we will calculate the square root of 1156 by repeated subtraction method and prime factorization method and solve a few interesting problems.

What is the Square Root of 198?

The square root of 198, (or root 198), is the number which when multiplied by itself gives the product as 198. Therefore, the square root of 198 = √198 = 3 √22 = 14.071247279470288.

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Is Square Root of 1296 Rational or Irrational?

The square roots of 1296 are +36 and -36. Both numbers are integers and all integers are rational numbers. Therefore, the square root of 1296 is a rational number.

How to Find Square Root of 198?

Value of √198 by Long Division Method

Therefore, the square root of 198 by long division method is 14.0 approximately.

What Is The Square Root of 1296?

Now we will find the square root of 1296 using the prime factorization and long division methods.

Square Root of 1296 by Prime Factorization Method

We will now find the square root of 1296 using the long division method:

So, we get the square root of √1296 = 36 by the long division method.

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Is the Square Root of 1156 Rational or Irrational?

The actual value of √198 is undetermined. The value of √198 up to 25 decimal places is 14.07124727947028866369689. Hence, the square root of 198 is an irrational number.

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FAQs on the Square Root of 198

The square root of 198 is 14.07124.

Why is the Square Root of 198 an Irrational Number?

Upon prime factorizing 198 i.e. 21 × 32 × 111, 2 is in odd power. Therefore, the square root of 198 is irrational.

What is the Square of the Square Root of 198?

The square of the square root of 198 is the number 198 itself i.e. (√198)2 = (198)2/2 = 198.

If the Square Root of 198 is 14. 071. Find the Value of the Square Root of 1.

Let us represent √1.98 in p/q form i.e. √(198/100) = 1.98/10 = 1.407. Hence, the value of √1.98 = 1.407

What is the Square Root of 198 in Simplest Radical Form?

We need to express 198 as the product of its prime factors i.e. 198 = 2 × 3 × 3 × 11. Therefore, √198 = √2 × 3 × 3 × 11 = 3 √22. Thus, the square root of 198 in the lowest radical form is 3 √22.

Evaluate 13 plus 11 square root 198

The given expression is 13 + 11 √198. We know that the square root of 198 is 14.071. Therefore, 13 + 11 √198 = 13 + 11 × 14.071 = 13 + 154.784 = 167.784

The square root of 198 is expressed as √198 in the radical form and as (198)½ or (198)0.5 in the exponent form. The square root of 198 rounded up to 9 decimal places is 14.071247279. It is the positive solution of the equation x2 = 198. We can express the square root of 198 in its lowest radical form as 3 √22.

How to Find the Square Root of 1156?

The square root of 1156 can be calculated using different methods such as prime factorization or the repeated subtraction method.

Square Root of 1156 by Repeated Subtraction Method

Square Root of 198 Solved Examples

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FAQs on Square Root of 1156

The square root of  is ± 34

Is 1156 a perfect square?

The numbers ending with 0, 1, 4, 5, 6, or 9 at the units place are perfect squares. 1156 has the roots 34, which is a whole number. Thus 1156 is a perfect square.

Is the square root of 1156 an irrational number?

No, the square root of 1156 is a rational number. Since √1156 = ± 34 is a whole number, we can express it as the ratio of 34/1 and -34/1.

What is the square root of 1156 by prime factorization method?

1156 = 2 × 2 ×  17 × 17 and √1156 =  √(2 × 2 ×  17 × 17 ) ⇒ √1156 = 2 × 17 = 34

What are the methods to find the square root of 1156?

We can find the square root of  using prime factorization method, or repeated subtraction method.

FAQs on Square Root of 1296

The square root of negative numbers is imaginary because squares of both positive and negative numbers result in positive numbers.
The square root of -1296 is represented as ±36i. (where i = √-1)

What is the square of 1296?

Square of the number 1296 is (1296)2 = 16,79,616

What is the square root of 1296 in prime factorization form?

The square root of 1296 is √1296 = 36.
Now, the prime factorization of 36 = 2 × 2 × 3 × 3

Can we find the square root of 1296 using the approximation method?

No, we can’t find the square root of 1296 using the approximation method because the number 1296 is a perfect square and this method cannot be used in the case if the given number is a perfect square.