Simplify Square Root of 81024

Here we will show you two methods that you can use to simplify the square root of 81024. In other words, we will show you how to find the square root of 81024 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.

√81024 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 81024 to simplify the square root of 81024. 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 81024. The factors of 81024 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 211, 384, 422, 633, 844, 1266, 1688, 2532, 3376, 5064, 6752, 10128, 13504, 20256, 27008, 40512, and 81024. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 81024 divided by the greatest perfect square from the list of all factors of 81024. We determined above that the greatest perfect square from the list of all factors of 81024 is 64. Furthermore, 81024 divided by 64 is 1266, therefore B equals 1266.

Now we have A and B and can get our answer to 81024 in its simplest radical form as follows:

√81024 = A√B

√81024 = 8√1266

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 81024 to simplify the square root of 81024 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 81024 and then take the square root of that product. The prime factors that multiply together to make 81024 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 211. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 = 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Divide 81024 by the number (A) squared. 8 squared is 64 and 81024 divided by 64 is 1266. Therefore, B equals 1266.

Once again we have A and B and can get our answer to 81024 in its simplest radical form as follows:

√81024 = A√B

√81024 = 8√1266

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