Simplify Square Root of 92976

Here we will show you two methods that you can use to simplify the square root of 92976. In other words, we will show you how to find the square root of 92976 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.

√92976 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 92976 to simplify the square root of 92976. 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 92976. The factors of 92976 are 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 78, 104, 149, 156, 208, 298, 312, 447, 596, 624, 894, 1192, 1788, 1937, 2384, 3576, 3874, 5811, 7152, 7748, 11622, 15496, 23244, 30992, 46488, and 92976. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 92976 divided by the greatest perfect square from the list of all factors of 92976. We determined above that the greatest perfect square from the list of all factors of 92976 is 16. Furthermore, 92976 divided by 16 is 5811, therefore B equals 5811.

Now we have A and B and can get our answer to 92976 in its simplest radical form as follows:

√92976 = A√B

√92976 = 4√5811

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 92976 to simplify the square root of 92976 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 92976 and then take the square root of that product. The prime factors that multiply together to make 92976 are 2 x 2 x 2 x 2 x 3 x 13 x 149. 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 92976 by the number (A) squared. 4 squared is 16 and 92976 divided by 16 is 5811. Therefore, B equals 5811.

Once again we have A and B and can get our answer to 92976 in its simplest radical form as follows:

√92976 = A√B

√92976 = 4√5811

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