Simplify Square Root of 57564

Here we will show you two methods that you can use to simplify the square root of 57564. In other words, we will show you how to find the square root of 57564 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.

√57564 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 57564 to simplify the square root of 57564. 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 57564. The factors of 57564 are 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 27, 36, 39, 41, 52, 54, 78, 82, 108, 117, 123, 156, 164, 234, 246, 351, 369, 468, 492, 533, 702, 738, 1066, 1107, 1404, 1476, 1599, 2132, 2214, 3198, 4428, 4797, 6396, 9594, 14391, 19188, 28782, and 57564. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 57564 divided by the greatest perfect square from the list of all factors of 57564. We determined above that the greatest perfect square from the list of all factors of 57564 is 36. Furthermore, 57564 divided by 36 is 1599, therefore B equals 1599.

Now we have A and B and can get our answer to 57564 in its simplest radical form as follows:

√57564 = A√B

√57564 = 6√1599

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 57564 to simplify the square root of 57564 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 57564 and then take the square root of that product. The prime factors that multiply together to make 57564 are 2 x 2 x 3 x 3 x 3 x 13 x 41. When we strip out the pairs only, we get 2 x 2 x 3 x 3 = 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Divide 57564 by the number (A) squared. 6 squared is 36 and 57564 divided by 36 is 1599. Therefore, B equals 1599.

Once again we have A and B and can get our answer to 57564 in its simplest radical form as follows:

√57564 = A√B

√57564 = 6√1599

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

Simplify Square Root of 57565
Here is the next square root on our list that we have simplifed for you.