Simplify Square Root of 93888

Here we will show you two methods that you can use to simplify the square root of 93888. In other words, we will show you how to find the square root of 93888 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.

√93888 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 93888 to simplify the square root of 93888. 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 93888. The factors of 93888 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 144, 163, 192, 288, 326, 489, 576, 652, 978, 1304, 1467, 1956, 2608, 2934, 3912, 5216, 5868, 7824, 10432, 11736, 15648, 23472, 31296, 46944, and 93888. Furthermore, the greatest perfect square on this list is 576 and the square root of 576 is 24. Therefore, A equals 24.

B = Calculate 93888 divided by the greatest perfect square from the list of all factors of 93888. We determined above that the greatest perfect square from the list of all factors of 93888 is 576. Furthermore, 93888 divided by 576 is 163, therefore B equals 163.

Now we have A and B and can get our answer to 93888 in its simplest radical form as follows:

√93888 = A√B

√93888 = 24√163

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 93888 to simplify the square root of 93888 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 93888 and then take the square root of that product. The prime factors that multiply together to make 93888 are 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 163. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 = 576 and the square root of 576 is 24. Therefore, A equals 24.

B = Divide 93888 by the number (A) squared. 24 squared is 576 and 93888 divided by 576 is 163. Therefore, B equals 163.

Once again we have A and B and can get our answer to 93888 in its simplest radical form as follows:

√93888 = A√B

√93888 = 24√163

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