Simplify Square Root of 98928

Here we will show you two methods that you can use to simplify the square root of 98928. In other words, we will show you how to find the square root of 98928 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.

√98928 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 98928 to simplify the square root of 98928. 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 98928. The factors of 98928 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 216, 229, 432, 458, 687, 916, 1374, 1832, 2061, 2748, 3664, 4122, 5496, 6183, 8244, 10992, 12366, 16488, 24732, 32976, 49464, and 98928. Furthermore, the greatest perfect square on this list is 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Calculate 98928 divided by the greatest perfect square from the list of all factors of 98928. We determined above that the greatest perfect square from the list of all factors of 98928 is 144. Furthermore, 98928 divided by 144 is 687, therefore B equals 687.

Now we have A and B and can get our answer to 98928 in its simplest radical form as follows:

√98928 = A√B

√98928 = 12√687

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 98928 to simplify the square root of 98928 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 98928 and then take the square root of that product. The prime factors that multiply together to make 98928 are 2 x 2 x 2 x 2 x 3 x 3 x 3 x 229. 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 98928 by the number (A) squared. 12 squared is 144 and 98928 divided by 144 is 687. Therefore, B equals 687.

Once again we have A and B and can get our answer to 98928 in its simplest radical form as follows:

√98928 = A√B

√98928 = 12√687

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