Simplify Square Root of 95936

Here we will show you two methods that you can use to simplify the square root of 95936. In other words, we will show you how to find the square root of 95936 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.

√95936 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 95936 to simplify the square root of 95936. 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 95936. The factors of 95936 are 1, 2, 4, 8, 16, 32, 64, 1499, 2998, 5996, 11992, 23984, 47968, and 95936. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 95936 divided by the greatest perfect square from the list of all factors of 95936. We determined above that the greatest perfect square from the list of all factors of 95936 is 64. Furthermore, 95936 divided by 64 is 1499, therefore B equals 1499.

Now we have A and B and can get our answer to 95936 in its simplest radical form as follows:

√95936 = A√B

√95936 = 8√1499

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 95936 to simplify the square root of 95936 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 95936 and then take the square root of that product. The prime factors that multiply together to make 95936 are 2 x 2 x 2 x 2 x 2 x 2 x 1499. 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 95936 by the number (A) squared. 8 squared is 64 and 95936 divided by 64 is 1499. Therefore, B equals 1499.

Once again we have A and B and can get our answer to 95936 in its simplest radical form as follows:

√95936 = A√B

√95936 = 8√1499

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Simplify Square Root of 95937
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