Simplify Square Root of 8712

Here we will show you two methods that you can use to simplify the square root of 8712. In other words, we will show you how to find the square root of 8712 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.

√8712 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 8712 to simplify the square root of 8712. 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 8712. The factors of 8712 are 1, 2, 3, 4, 6, 8, 9, 11, 12, 18, 22, 24, 33, 36, 44, 66, 72, 88, 99, 121, 132, 198, 242, 264, 363, 396, 484, 726, 792, 968, 1089, 1452, 2178, 2904, 4356, and 8712. Furthermore, the greatest perfect square on this list is 4356 and the square root of 4356 is 66. Therefore, A equals 66.

B = Calculate 8712 divided by the greatest perfect square from the list of all factors of 8712. We determined above that the greatest perfect square from the list of all factors of 8712 is 4356. Furthermore, 8712 divided by 4356 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 8712 in its simplest radical form as follows:

√8712 = A√B

√8712 = 66√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 8712 to simplify the square root of 8712 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 8712 and then take the square root of that product. The prime factors that multiply together to make 8712 are 2 x 2 x 2 x 3 x 3 x 11 x 11. When we strip out the pairs only, we get 2 x 2 x 3 x 3 x 11 x 11 = 4356 and the square root of 4356 is 66. Therefore, A equals 66.

B = Divide 8712 by the number (A) squared. 66 squared is 4356 and 8712 divided by 4356 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 8712 in its simplest radical form as follows:

√8712 = A√B

√8712 = 66√2

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