Simplify Square Root of 81216

Here we will show you two methods that you can use to simplify the square root of 81216. In other words, we will show you how to find the square root of 81216 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.

√81216 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 81216 to simplify the square root of 81216. 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 81216. The factors of 81216 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 47, 48, 54, 64, 72, 94, 96, 108, 141, 144, 188, 192, 216, 282, 288, 376, 423, 432, 564, 576, 752, 846, 864, 1128, 1269, 1504, 1692, 1728, 2256, 2538, 3008, 3384, 4512, 5076, 6768, 9024, 10152, 13536, 20304, 27072, 40608, and 81216. Furthermore, the greatest perfect square on this list is 576 and the square root of 576 is 24. Therefore, A equals 24.

B = Calculate 81216 divided by the greatest perfect square from the list of all factors of 81216. We determined above that the greatest perfect square from the list of all factors of 81216 is 576. Furthermore, 81216 divided by 576 is 141, therefore B equals 141.

Now we have A and B and can get our answer to 81216 in its simplest radical form as follows:

√81216 = A√B

√81216 = 24√141

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 81216 to simplify the square root of 81216 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 81216 and then take the square root of that product. The prime factors that multiply together to make 81216 are 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 47. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 = 576 and the square root of 576 is 24. Therefore, A equals 24.

B = Divide 81216 by the number (A) squared. 24 squared is 576 and 81216 divided by 576 is 141. Therefore, B equals 141.

Once again we have A and B and can get our answer to 81216 in its simplest radical form as follows:

√81216 = A√B

√81216 = 24√141

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