Simplify Square Root of 91136

Here we will show you two methods that you can use to simplify the square root of 91136. In other words, we will show you how to find the square root of 91136 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.

√91136 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 91136 to simplify the square root of 91136. 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 91136. The factors of 91136 are 1, 2, 4, 8, 16, 32, 64, 89, 128, 178, 256, 356, 512, 712, 1024, 1424, 2848, 5696, 11392, 22784, 45568, and 91136. Furthermore, the greatest perfect square on this list is 1024 and the square root of 1024 is 32. Therefore, A equals 32.

B = Calculate 91136 divided by the greatest perfect square from the list of all factors of 91136. We determined above that the greatest perfect square from the list of all factors of 91136 is 1024. Furthermore, 91136 divided by 1024 is 89, therefore B equals 89.

Now we have A and B and can get our answer to 91136 in its simplest radical form as follows:

√91136 = A√B

√91136 = 32√89

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 91136 to simplify the square root of 91136 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 91136 and then take the square root of that product. The prime factors that multiply together to make 91136 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 89. 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 91136 by the number (A) squared. 32 squared is 1024 and 91136 divided by 1024 is 89. Therefore, B equals 89.

Once again we have A and B and can get our answer to 91136 in its simplest radical form as follows:

√91136 = A√B

√91136 = 32√89

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Simplify Square Root of 91137
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