Simplify Square Root of 23088

Here we will show you two methods that you can use to simplify the square root of 23088. In other words, we will show you how to find the square root of 23088 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.

√23088 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 23088 to simplify the square root of 23088. 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 23088. The factors of 23088 are 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 37, 39, 48, 52, 74, 78, 104, 111, 148, 156, 208, 222, 296, 312, 444, 481, 592, 624, 888, 962, 1443, 1776, 1924, 2886, 3848, 5772, 7696, 11544, and 23088. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 23088 divided by the greatest perfect square from the list of all factors of 23088. We determined above that the greatest perfect square from the list of all factors of 23088 is 16. Furthermore, 23088 divided by 16 is 1443, therefore B equals 1443.

Now we have A and B and can get our answer to 23088 in its simplest radical form as follows:

√23088 = A√B

√23088 = 4√1443

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 23088 to simplify the square root of 23088 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 23088 and then take the square root of that product. The prime factors that multiply together to make 23088 are 2 x 2 x 2 x 2 x 3 x 13 x 37. When we strip out the pairs only, we get 2 x 2 x 2 x 2 = 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Divide 23088 by the number (A) squared. 4 squared is 16 and 23088 divided by 16 is 1443. Therefore, B equals 1443.

Once again we have A and B and can get our answer to 23088 in its simplest radical form as follows:

√23088 = A√B

√23088 = 4√1443

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

Simplify Square Root of 23089
Here is the next square root on our list that we have simplifed for you.