Simplify Square Root of 96912

Here we will show you two methods that you can use to simplify the square root of 96912. In other words, we will show you how to find the square root of 96912 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.

√96912 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 96912 to simplify the square root of 96912. 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 96912. The factors of 96912 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 673, 1346, 2019, 2692, 4038, 5384, 6057, 8076, 10768, 12114, 16152, 24228, 32304, 48456, and 96912. Furthermore, the greatest perfect square on this list is 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Calculate 96912 divided by the greatest perfect square from the list of all factors of 96912. We determined above that the greatest perfect square from the list of all factors of 96912 is 144. Furthermore, 96912 divided by 144 is 673, therefore B equals 673.

Now we have A and B and can get our answer to 96912 in its simplest radical form as follows:

√96912 = A√B

√96912 = 12√673

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 96912 to simplify the square root of 96912 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 96912 and then take the square root of that product. The prime factors that multiply together to make 96912 are 2 x 2 x 2 x 2 x 3 x 3 x 673. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 3 x 3 = 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Divide 96912 by the number (A) squared. 12 squared is 144 and 96912 divided by 144 is 673. Therefore, B equals 673.

Once again we have A and B and can get our answer to 96912 in its simplest radical form as follows:

√96912 = A√B

√96912 = 12√673

Simplify Square Root
Please enter another square root in the box below for us to simplify.

Simplify Square Root of 96913
Here is the next square root on our list that we have simplifed for you.