Simplify Square Root of 81648

Here we will show you two methods that you can use to simplify the square root of 81648. In other words, we will show you how to find the square root of 81648 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.

√81648 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 81648 to simplify the square root of 81648. 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 81648. The factors of 81648 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 27, 28, 36, 42, 48, 54, 56, 63, 72, 81, 84, 108, 112, 126, 144, 162, 168, 189, 216, 243, 252, 324, 336, 378, 432, 486, 504, 567, 648, 729, 756, 972, 1008, 1134, 1296, 1458, 1512, 1701, 1944, 2268, 2916, 3024, 3402, 3888, 4536, 5103, 5832, 6804, 9072, 10206, 11664, 13608, 20412, 27216, 40824, and 81648. Furthermore, the greatest perfect square on this list is 11664 and the square root of 11664 is 108. Therefore, A equals 108.

B = Calculate 81648 divided by the greatest perfect square from the list of all factors of 81648. We determined above that the greatest perfect square from the list of all factors of 81648 is 11664. Furthermore, 81648 divided by 11664 is 7, therefore B equals 7.

Now we have A and B and can get our answer to 81648 in its simplest radical form as follows:

√81648 = A√B

√81648 = 108√7

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 81648 to simplify the square root of 81648 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 81648 and then take the square root of that product. The prime factors that multiply together to make 81648 are 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3 x 7. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3 = 11664 and the square root of 11664 is 108. Therefore, A equals 108.

B = Divide 81648 by the number (A) squared. 108 squared is 11664 and 81648 divided by 11664 is 7. Therefore, B equals 7.

Once again we have A and B and can get our answer to 81648 in its simplest radical form as follows:

√81648 = A√B

√81648 = 108√7

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Simplify Square Root of 81649
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