Simplify Square Root of 81536

Here we will show you two methods that you can use to simplify the square root of 81536. In other words, we will show you how to find the square root of 81536 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.

√81536 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 81536 to simplify the square root of 81536. 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 81536. The factors of 81536 are 1, 2, 4, 7, 8, 13, 14, 16, 26, 28, 32, 49, 52, 56, 64, 91, 98, 104, 112, 128, 182, 196, 208, 224, 364, 392, 416, 448, 637, 728, 784, 832, 896, 1274, 1456, 1568, 1664, 2548, 2912, 3136, 5096, 5824, 6272, 10192, 11648, 20384, 40768, and 81536. Furthermore, the greatest perfect square on this list is 3136 and the square root of 3136 is 56. Therefore, A equals 56.

B = Calculate 81536 divided by the greatest perfect square from the list of all factors of 81536. We determined above that the greatest perfect square from the list of all factors of 81536 is 3136. Furthermore, 81536 divided by 3136 is 26, therefore B equals 26.

Now we have A and B and can get our answer to 81536 in its simplest radical form as follows:

√81536 = A√B

√81536 = 56√26

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 81536 to simplify the square root of 81536 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 81536 and then take the square root of that product. The prime factors that multiply together to make 81536 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 7 x 7 x 13. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 7 x 7 = 3136 and the square root of 3136 is 56. Therefore, A equals 56.

B = Divide 81536 by the number (A) squared. 56 squared is 3136 and 81536 divided by 3136 is 26. Therefore, B equals 26.

Once again we have A and B and can get our answer to 81536 in its simplest radical form as follows:

√81536 = A√B

√81536 = 56√26

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