Simplify Square Root of 93216

Here we will show you two methods that you can use to simplify the square root of 93216. In other words, we will show you how to find the square root of 93216 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.

√93216 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 93216 to simplify the square root of 93216. 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 93216. The factors of 93216 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 971, 1942, 2913, 3884, 5826, 7768, 11652, 15536, 23304, 31072, 46608, and 93216. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 93216 divided by the greatest perfect square from the list of all factors of 93216. We determined above that the greatest perfect square from the list of all factors of 93216 is 16. Furthermore, 93216 divided by 16 is 5826, therefore B equals 5826.

Now we have A and B and can get our answer to 93216 in its simplest radical form as follows:

√93216 = A√B

√93216 = 4√5826

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 93216 to simplify the square root of 93216 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 93216 and then take the square root of that product. The prime factors that multiply together to make 93216 are 2 x 2 x 2 x 2 x 2 x 3 x 971. 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 93216 by the number (A) squared. 4 squared is 16 and 93216 divided by 16 is 5826. Therefore, B equals 5826.

Once again we have A and B and can get our answer to 93216 in its simplest radical form as follows:

√93216 = A√B

√93216 = 4√5826

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