Simplify Square Root of 36517

Here we will show you two methods that you can use to simplify the square root of 36517. In other words, we will show you how to find the square root of 36517 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.

√36517 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 36517 to simplify the square root of 36517. 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 36517. The factors of 36517 are 1, 13, 53, 689, 2809, and 36517. Furthermore, the greatest perfect square on this list is 2809 and the square root of 2809 is 53. Therefore, A equals 53.

B = Calculate 36517 divided by the greatest perfect square from the list of all factors of 36517. We determined above that the greatest perfect square from the list of all factors of 36517 is 2809. Furthermore, 36517 divided by 2809 is 13, therefore B equals 13.

Now we have A and B and can get our answer to 36517 in its simplest radical form as follows:

√36517 = A√B

√36517 = 53√13

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 36517 to simplify the square root of 36517 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 36517 and then take the square root of that product. The prime factors that multiply together to make 36517 are 13 x 53 x 53. When we strip out the pairs only, we get 53 x 53 = 2809 and the square root of 2809 is 53. Therefore, A equals 53.

B = Divide 36517 by the number (A) squared. 53 squared is 2809 and 36517 divided by 2809 is 13. Therefore, B equals 13.

Once again we have A and B and can get our answer to 36517 in its simplest radical form as follows:

√36517 = A√B

√36517 = 53√13

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

Simplify Square Root of 36518
Here is the next square root on our list that we have simplifed for you.