Simplify Square Root of 93288

Here we will show you two methods that you can use to simplify the square root of 93288. In other words, we will show you how to find the square root of 93288 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.

√93288 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 93288 to simplify the square root of 93288. 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 93288. The factors of 93288 are 1, 2, 3, 4, 6, 8, 12, 13, 23, 24, 26, 39, 46, 52, 69, 78, 92, 104, 138, 156, 169, 184, 276, 299, 312, 338, 507, 552, 598, 676, 897, 1014, 1196, 1352, 1794, 2028, 2392, 3588, 3887, 4056, 7176, 7774, 11661, 15548, 23322, 31096, 46644, and 93288. Furthermore, the greatest perfect square on this list is 676 and the square root of 676 is 26. Therefore, A equals 26.

B = Calculate 93288 divided by the greatest perfect square from the list of all factors of 93288. We determined above that the greatest perfect square from the list of all factors of 93288 is 676. Furthermore, 93288 divided by 676 is 138, therefore B equals 138.

Now we have A and B and can get our answer to 93288 in its simplest radical form as follows:

√93288 = A√B

√93288 = 26√138

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 93288 to simplify the square root of 93288 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 93288 and then take the square root of that product. The prime factors that multiply together to make 93288 are 2 x 2 x 2 x 3 x 13 x 13 x 23. When we strip out the pairs only, we get 2 x 2 x 13 x 13 = 676 and the square root of 676 is 26. Therefore, A equals 26.

B = Divide 93288 by the number (A) squared. 26 squared is 676 and 93288 divided by 676 is 138. Therefore, B equals 138.

Once again we have A and B and can get our answer to 93288 in its simplest radical form as follows:

√93288 = A√B

√93288 = 26√138

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