Simplify Square Root of 92592

Here we will show you two methods that you can use to simplify the square root of 92592. In other words, we will show you how to find the square root of 92592 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.

√92592 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 92592 to simplify the square root of 92592. 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 92592. The factors of 92592 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 643, 1286, 1929, 2572, 3858, 5144, 5787, 7716, 10288, 11574, 15432, 23148, 30864, 46296, and 92592. Furthermore, the greatest perfect square on this list is 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Calculate 92592 divided by the greatest perfect square from the list of all factors of 92592. We determined above that the greatest perfect square from the list of all factors of 92592 is 144. Furthermore, 92592 divided by 144 is 643, therefore B equals 643.

Now we have A and B and can get our answer to 92592 in its simplest radical form as follows:

√92592 = A√B

√92592 = 12√643

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 92592 to simplify the square root of 92592 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 92592 and then take the square root of that product. The prime factors that multiply together to make 92592 are 2 x 2 x 2 x 2 x 3 x 3 x 643. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 3 x 3 = 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Divide 92592 by the number (A) squared. 12 squared is 144 and 92592 divided by 144 is 643. Therefore, B equals 643.

Once again we have A and B and can get our answer to 92592 in its simplest radical form as follows:

√92592 = A√B

√92592 = 12√643

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