Simplify Square Root of 84992

Here we will show you two methods that you can use to simplify the square root of 84992. In other words, we will show you how to find the square root of 84992 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.

√84992 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 84992 to simplify the square root of 84992. 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 84992. The factors of 84992 are 1, 2, 4, 8, 16, 32, 64, 83, 128, 166, 256, 332, 512, 664, 1024, 1328, 2656, 5312, 10624, 21248, 42496, and 84992. Furthermore, the greatest perfect square on this list is 1024 and the square root of 1024 is 32. Therefore, A equals 32.

B = Calculate 84992 divided by the greatest perfect square from the list of all factors of 84992. We determined above that the greatest perfect square from the list of all factors of 84992 is 1024. Furthermore, 84992 divided by 1024 is 83, therefore B equals 83.

Now we have A and B and can get our answer to 84992 in its simplest radical form as follows:

√84992 = A√B

√84992 = 32√83

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 84992 to simplify the square root of 84992 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 84992 and then take the square root of that product. The prime factors that multiply together to make 84992 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 83. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 1024 and the square root of 1024 is 32. Therefore, A equals 32.

B = Divide 84992 by the number (A) squared. 32 squared is 1024 and 84992 divided by 1024 is 83. Therefore, B equals 83.

Once again we have A and B and can get our answer to 84992 in its simplest radical form as follows:

√84992 = A√B

√84992 = 32√83

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