Simplify Square Root of 9971

Here we will show you two methods that you can use to simplify the square root of 9971. In other words, we will show you how to find the square root of 9971 in its simplest radical form using two different methods.

To be more specific, we have created an illustration below showing what we want to calculate. Our goal is to make "A" outside the radical (√) as large as possible, and "B" inside the radical (√) as small as possible.

√9971 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 9971 to simplify the square root of 9971. This is how to calculate A and B using this method:

A = Calculate the square root of the greatest perfect square from the list of all factors of 9971. The factors of 9971 are 1, 13, 59, 169, 767, and 9971. Furthermore, the greatest perfect square on this list is 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Calculate 9971 divided by the greatest perfect square from the list of all factors of 9971. We determined above that the greatest perfect square from the list of all factors of 9971 is 169. Furthermore, 9971 divided by 169 is 59, therefore B equals 59.

Now we have A and B and can get our answer to 9971 in its simplest radical form as follows:

√9971 = A√B

√9971 = 13√59

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 9971 to simplify the square root of 9971 to its simplest form possible. This is how to calculate A and B using this method:

A = Multiply all the double prime factors (pairs) of 9971 and then take the square root of that product. The prime factors that multiply together to make 9971 are 13 x 13 x 59. When we strip out the pairs only, we get 13 x 13 = 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Divide 9971 by the number (A) squared. 13 squared is 169 and 9971 divided by 169 is 59. Therefore, B equals 59.

Once again we have A and B and can get our answer to 9971 in its simplest radical form as follows:

√9971 = A√B

√9971 = 13√59

Simplify Square Root
Please enter another square root in the box below for us to simplify.

Simplify Square Root of 9972
Here is the next square root on our list that we have simplifed for you.