Simplify Square Root of 93312

Here we will show you two methods that you can use to simplify the square root of 93312. In other words, we will show you how to find the square root of 93312 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.

√93312 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 93312 to simplify the square root of 93312. 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 93312. The factors of 93312 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 128, 144, 162, 192, 216, 243, 288, 324, 384, 432, 486, 576, 648, 729, 864, 972, 1152, 1296, 1458, 1728, 1944, 2592, 2916, 3456, 3888, 5184, 5832, 7776, 10368, 11664, 15552, 23328, 31104, 46656, and 93312. Furthermore, the greatest perfect square on this list is 46656 and the square root of 46656 is 216. Therefore, A equals 216.

B = Calculate 93312 divided by the greatest perfect square from the list of all factors of 93312. We determined above that the greatest perfect square from the list of all factors of 93312 is 46656. Furthermore, 93312 divided by 46656 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 93312 in its simplest radical form as follows:

√93312 = A√B

√93312 = 216√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 93312 to simplify the square root of 93312 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 93312 and then take the square root of that product. The prime factors that multiply together to make 93312 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3 = 46656 and the square root of 46656 is 216. Therefore, A equals 216.

B = Divide 93312 by the number (A) squared. 216 squared is 46656 and 93312 divided by 46656 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 93312 in its simplest radical form as follows:

√93312 = A√B

√93312 = 216√2

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Simplify Square Root of 93313
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