Simplify Square Root of 37908

Here we will show you two methods that you can use to simplify the square root of 37908. In other words, we will show you how to find the square root of 37908 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.

√37908 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 37908 to simplify the square root of 37908. 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 37908. The factors of 37908 are 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 27, 36, 39, 52, 54, 78, 81, 108, 117, 156, 162, 234, 243, 324, 351, 468, 486, 702, 729, 972, 1053, 1404, 1458, 2106, 2916, 3159, 4212, 6318, 9477, 12636, 18954, and 37908. Furthermore, the greatest perfect square on this list is 2916 and the square root of 2916 is 54. Therefore, A equals 54.

B = Calculate 37908 divided by the greatest perfect square from the list of all factors of 37908. We determined above that the greatest perfect square from the list of all factors of 37908 is 2916. Furthermore, 37908 divided by 2916 is 13, therefore B equals 13.

Now we have A and B and can get our answer to 37908 in its simplest radical form as follows:

√37908 = A√B

√37908 = 54√13

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 37908 to simplify the square root of 37908 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 37908 and then take the square root of that product. The prime factors that multiply together to make 37908 are 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3 x 13. When we strip out the pairs only, we get 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3 = 2916 and the square root of 2916 is 54. Therefore, A equals 54.

B = Divide 37908 by the number (A) squared. 54 squared is 2916 and 37908 divided by 2916 is 13. Therefore, B equals 13.

Once again we have A and B and can get our answer to 37908 in its simplest radical form as follows:

√37908 = A√B

√37908 = 54√13

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

Simplify Square Root of 37909
Here is the next square root on our list that we have simplifed for you.