Simplify Square Root of 81792

Here we will show you two methods that you can use to simplify the square root of 81792. In other words, we will show you how to find the square root of 81792 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.

√81792 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 81792 to simplify the square root of 81792. 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 81792. The factors of 81792 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 71, 72, 96, 128, 142, 144, 192, 213, 284, 288, 384, 426, 568, 576, 639, 852, 1136, 1152, 1278, 1704, 2272, 2556, 3408, 4544, 5112, 6816, 9088, 10224, 13632, 20448, 27264, 40896, and 81792. Furthermore, the greatest perfect square on this list is 576 and the square root of 576 is 24. Therefore, A equals 24.

B = Calculate 81792 divided by the greatest perfect square from the list of all factors of 81792. We determined above that the greatest perfect square from the list of all factors of 81792 is 576. Furthermore, 81792 divided by 576 is 142, therefore B equals 142.

Now we have A and B and can get our answer to 81792 in its simplest radical form as follows:

√81792 = A√B

√81792 = 24√142

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 81792 to simplify the square root of 81792 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 81792 and then take the square root of that product. The prime factors that multiply together to make 81792 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 71. 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 81792 by the number (A) squared. 24 squared is 576 and 81792 divided by 576 is 142. Therefore, B equals 142.

Once again we have A and B and can get our answer to 81792 in its simplest radical form as follows:

√81792 = A√B

√81792 = 24√142

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