Simplify Square Root of 39528

Here we will show you two methods that you can use to simplify the square root of 39528. In other words, we will show you how to find the square root of 39528 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.

√39528 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 39528 to simplify the square root of 39528. 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 39528. The factors of 39528 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 61, 72, 81, 108, 122, 162, 183, 216, 244, 324, 366, 488, 549, 648, 732, 1098, 1464, 1647, 2196, 3294, 4392, 4941, 6588, 9882, 13176, 19764, and 39528. Furthermore, the greatest perfect square on this list is 324 and the square root of 324 is 18. Therefore, A equals 18.

B = Calculate 39528 divided by the greatest perfect square from the list of all factors of 39528. We determined above that the greatest perfect square from the list of all factors of 39528 is 324. Furthermore, 39528 divided by 324 is 122, therefore B equals 122.

Now we have A and B and can get our answer to 39528 in its simplest radical form as follows:

√39528 = A√B

√39528 = 18√122

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 39528 to simplify the square root of 39528 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 39528 and then take the square root of that product. The prime factors that multiply together to make 39528 are 2 x 2 x 2 x 3 x 3 x 3 x 3 x 61. When we strip out the pairs only, we get 2 x 2 x 3 x 3 x 3 x 3 = 324 and the square root of 324 is 18. Therefore, A equals 18.

B = Divide 39528 by the number (A) squared. 18 squared is 324 and 39528 divided by 324 is 122. Therefore, B equals 122.

Once again we have A and B and can get our answer to 39528 in its simplest radical form as follows:

√39528 = A√B

√39528 = 18√122

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

Simplify Square Root of 39529
Here is the next square root on our list that we have simplifed for you.