Simplify Square Root of 88752

Here we will show you two methods that you can use to simplify the square root of 88752. In other words, we will show you how to find the square root of 88752 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.

√88752 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 88752 to simplify the square root of 88752. 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 88752. The factors of 88752 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 43, 48, 86, 129, 172, 258, 344, 516, 688, 1032, 1849, 2064, 3698, 5547, 7396, 11094, 14792, 22188, 29584, 44376, and 88752. Furthermore, the greatest perfect square on this list is 29584 and the square root of 29584 is 172. Therefore, A equals 172.

B = Calculate 88752 divided by the greatest perfect square from the list of all factors of 88752. We determined above that the greatest perfect square from the list of all factors of 88752 is 29584. Furthermore, 88752 divided by 29584 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 88752 in its simplest radical form as follows:

√88752 = A√B

√88752 = 172√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 88752 to simplify the square root of 88752 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 88752 and then take the square root of that product. The prime factors that multiply together to make 88752 are 2 x 2 x 2 x 2 x 3 x 43 x 43. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 43 x 43 = 29584 and the square root of 29584 is 172. Therefore, A equals 172.

B = Divide 88752 by the number (A) squared. 172 squared is 29584 and 88752 divided by 29584 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 88752 in its simplest radical form as follows:

√88752 = A√B

√88752 = 172√3

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