Simplify Square Root of 97686

Here we will show you two methods that you can use to simplify the square root of 97686. In other words, we will show you how to find the square root of 97686 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.

√97686 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 97686 to simplify the square root of 97686. 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 97686. The factors of 97686 are 1, 2, 3, 6, 9, 18, 27, 54, 67, 81, 134, 162, 201, 243, 402, 486, 603, 729, 1206, 1458, 1809, 3618, 5427, 10854, 16281, 32562, 48843, and 97686. Furthermore, the greatest perfect square on this list is 729 and the square root of 729 is 27. Therefore, A equals 27.

B = Calculate 97686 divided by the greatest perfect square from the list of all factors of 97686. We determined above that the greatest perfect square from the list of all factors of 97686 is 729. Furthermore, 97686 divided by 729 is 134, therefore B equals 134.

Now we have A and B and can get our answer to 97686 in its simplest radical form as follows:

√97686 = A√B

√97686 = 27√134

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 97686 to simplify the square root of 97686 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 97686 and then take the square root of that product. The prime factors that multiply together to make 97686 are 2 x 3 x 3 x 3 x 3 x 3 x 3 x 67. When we strip out the pairs only, we get 3 x 3 x 3 x 3 x 3 x 3 = 729 and the square root of 729 is 27. Therefore, A equals 27.

B = Divide 97686 by the number (A) squared. 27 squared is 729 and 97686 divided by 729 is 134. Therefore, B equals 134.

Once again we have A and B and can get our answer to 97686 in its simplest radical form as follows:

√97686 = A√B

√97686 = 27√134

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

Simplify Square Root of 97687
Here is the next square root on our list that we have simplifed for you.