Simplify Square Root of 25992

Here we will show you two methods that you can use to simplify the square root of 25992. In other words, we will show you how to find the square root of 25992 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.

√25992 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 25992 to simplify the square root of 25992. 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 25992. The factors of 25992 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 19, 24, 36, 38, 57, 72, 76, 114, 152, 171, 228, 342, 361, 456, 684, 722, 1083, 1368, 1444, 2166, 2888, 3249, 4332, 6498, 8664, 12996, and 25992. Furthermore, the greatest perfect square on this list is 12996 and the square root of 12996 is 114. Therefore, A equals 114.

B = Calculate 25992 divided by the greatest perfect square from the list of all factors of 25992. We determined above that the greatest perfect square from the list of all factors of 25992 is 12996. Furthermore, 25992 divided by 12996 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 25992 in its simplest radical form as follows:

√25992 = A√B

√25992 = 114√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 25992 to simplify the square root of 25992 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 25992 and then take the square root of that product. The prime factors that multiply together to make 25992 are 2 x 2 x 2 x 3 x 3 x 19 x 19. When we strip out the pairs only, we get 2 x 2 x 3 x 3 x 19 x 19 = 12996 and the square root of 12996 is 114. Therefore, A equals 114.

B = Divide 25992 by the number (A) squared. 114 squared is 12996 and 25992 divided by 12996 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 25992 in its simplest radical form as follows:

√25992 = A√B

√25992 = 114√2

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