Simplify Square Root of 8112

Here we will show you two methods that you can use to simplify the square root of 8112. In other words, we will show you how to find the square root of 8112 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.

√8112 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 8112 to simplify the square root of 8112. 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 8112. The factors of 8112 are 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 78, 104, 156, 169, 208, 312, 338, 507, 624, 676, 1014, 1352, 2028, 2704, 4056, and 8112. Furthermore, the greatest perfect square on this list is 2704 and the square root of 2704 is 52. Therefore, A equals 52.

B = Calculate 8112 divided by the greatest perfect square from the list of all factors of 8112. We determined above that the greatest perfect square from the list of all factors of 8112 is 2704. Furthermore, 8112 divided by 2704 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 8112 in its simplest radical form as follows:

√8112 = A√B

√8112 = 52√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 8112 to simplify the square root of 8112 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 8112 and then take the square root of that product. The prime factors that multiply together to make 8112 are 2 x 2 x 2 x 2 x 3 x 13 x 13. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 13 x 13 = 2704 and the square root of 2704 is 52. Therefore, A equals 52.

B = Divide 8112 by the number (A) squared. 52 squared is 2704 and 8112 divided by 2704 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 8112 in its simplest radical form as follows:

√8112 = A√B

√8112 = 52√3

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Simplify Square Root of 8113
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