Simplify Square Root of 86756

Here we will show you two methods that you can use to simplify the square root of 86756. In other words, we will show you how to find the square root of 86756 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.

√86756 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 86756 to simplify the square root of 86756. 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 86756. The factors of 86756 are 1, 2, 4, 23, 41, 46, 82, 92, 164, 529, 943, 1058, 1886, 2116, 3772, 21689, 43378, and 86756. Furthermore, the greatest perfect square on this list is 2116 and the square root of 2116 is 46. Therefore, A equals 46.

B = Calculate 86756 divided by the greatest perfect square from the list of all factors of 86756. We determined above that the greatest perfect square from the list of all factors of 86756 is 2116. Furthermore, 86756 divided by 2116 is 41, therefore B equals 41.

Now we have A and B and can get our answer to 86756 in its simplest radical form as follows:

√86756 = A√B

√86756 = 46√41

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 86756 to simplify the square root of 86756 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 86756 and then take the square root of that product. The prime factors that multiply together to make 86756 are 2 x 2 x 23 x 23 x 41. When we strip out the pairs only, we get 2 x 2 x 23 x 23 = 2116 and the square root of 2116 is 46. Therefore, A equals 46.

B = Divide 86756 by the number (A) squared. 46 squared is 2116 and 86756 divided by 2116 is 41. Therefore, B equals 41.

Once again we have A and B and can get our answer to 86756 in its simplest radical form as follows:

√86756 = A√B

√86756 = 46√41

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

Simplify Square Root of 86757
Here is the next square root on our list that we have simplifed for you.