Root Calculator

General Root Calculator

In mathematics, the general root, or the nth root of a number a is another number b that when multiplied by itself n times, equals a. In equation format:

n√ = b
bn = 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 nth 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 √:

Estimating an nth Root

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.

In this article we’re going to calculate the square root of 17 and explore what the square root is and answer some of the common questions you might. We’ll also look at the different methods for calculating the square root of 17 (both with and without a computer/calculator).

Square Root of 17 Definition

In mathematical form we can show the square root of 17 using the radical sign, like this: √17. This is usually referred to as the square root of 17 in radical form.

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Want to quickly learn or refresh memory on how to calculate square root play this quick and informative video now!

So what is the square root? In this case, the square root of 17 is the quantity (which we will call q) that when multiplied by itself, will equal 17.

√17 = q × q = q2

Is 17 a Perfect Square?

In math, we refer to 17 being a perfect square if the square root of 17 is a whole number.

In this case, as we will see in the calculations below, we can see that 17 is not a perfect square.

To find out more about perfect squares, you can read about them and look at a list of 1000 of them in our What is a Perfect Square? article.

Is The Square Root of 17 Rational or Irrational?

A common question is to ask whether the square root of 17 is rational or irrational. Rational numbers can be written as a fraction and irrational numbers cannot.

A quick way to check this is to see if 17 is a perfect square. If it is, then it is a rational number. If it’s not a perfect square then it’s an irrational number.

We already know if 17 is a perfect square so we also can see that √17 is an irrational number.

Can the Square Root of 17 Be Simplified?

17 can be simplified only if you can make 17 inside the radical symbol smaller. This is a process that is called simplifying the surd. In this example square root of 17 cannot be simplified.

√17 is already in its simplest radical form.

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How to Calculate The Square Root of 17 with a Calculator

√17 ≈ 4.1231

How to Calculate the Square Root of 17 with a Computer

On a computer you can also calculate the square root of 17 using Excel, Numbers, or Google Sheets and the SQRT function, like so:

SQRT(17) ≈ 4.123105625618

What is the Square Root of 17 Rounded?

Sometimes you might need to round the square root of 17 down to a certain number of decimal places. Here are the solutions to that, if needed.

10th: √17 ≈ 4.1

100th: √17 ≈ 4.12

1000th: √17 ≈ 4.123

What is the Square Root of 17 as a Fraction?

We covered earlier in this article that only a rational number can be written as a fraction, and irrational numbers cannot.

Like we said above, since the square root of 17 is an irrational number, we cannot make it into an exact fraction. However, we can make it into an approximate fraction using the square root of 17 rounded to the nearest hundredth.

≈ 4 3/25

What is the Square Root of 17 Written with an Exponent?

All square root calculations can be converted to a number (called the base) with a fractional exponent. Let’s see how to do that with the square root of 17:

√b = b½

√17 = 17½

How to Find the Square Root of 17 Using Long Division

Finally, we can use the long division method to calculate the square root of 17. This is very useful for long division test problems and was how mathematicians would calculate the square root of a number before calculators and computers were invented.

Step 1

Set up 17 in pairs of two digits from right to left and attach one set of 00 because we want one decimal:

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Step 2

Starting with the first set: the largest perfect square less than or equal to 17 is 16, and the square root of 16 is 4 . Therefore, put 4 on top and 16 at the bottom like this:

Step 3

Calculate 17 minus 16 and put the difference below. Then move down the next set of numbers.

Step 4

Double the number in green on top: 4 × 2 = 8. Then, use 8 and the bottom number to make this problem:

8? × ? ≤ 100

The question marks are «blank» and the same «blank». With trial and error, we found the largest number «blank» can be is 1.

Now, enter 1 on top:

That’s it! The answer shown at the top in green. The square root of 17 with one digit decimal accuracy is 4.1.
Notice that the last two steps actually repeat the previous two. To add decimal places to your answe you can simply add more sets of 00 and repeat the last two steps.

Use the square root calculator below to find the square root of any imaginary or real number. See also in this web page a Square Root Table from 1 to 100 as well as the Babylonian Method or Hero’s Method.

The Babylonian Method also known as Hero’s Method

See below how to calculate the square root of 81 step-by-step using the Babylonian Method also known as Hero’s Method.

What is square root?

A square root of a number ‘a’ is a number x such that x2 = a, in other words, a number x whose square is a. For example, 9 is the square root of 81 because 92 = 9•9 = 81, -9 is square root of 81 because (-9)2 = (-9)•(-9) = 81.

Square Root Table 1-100

Square roots from 1 to 100 rounded to the nearest thousandth.

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