Simplify Square Root of 99520

Here we will show you two methods that you can use to simplify the square root of 99520. In other words, we will show you how to find the square root of 99520 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.

√99520 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 99520 to simplify the square root of 99520. 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 99520. The factors of 99520 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 311, 320, 622, 1244, 1555, 2488, 3110, 4976, 6220, 9952, 12440, 19904, 24880, 49760, and 99520. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 99520 divided by the greatest perfect square from the list of all factors of 99520. We determined above that the greatest perfect square from the list of all factors of 99520 is 64. Furthermore, 99520 divided by 64 is 1555, therefore B equals 1555.

Now we have A and B and can get our answer to 99520 in its simplest radical form as follows:

√99520 = A√B

√99520 = 8√1555

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 99520 to simplify the square root of 99520 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 99520 and then take the square root of that product. The prime factors that multiply together to make 99520 are 2 x 2 x 2 x 2 x 2 x 2 x 5 x 311. 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 99520 by the number (A) squared. 8 squared is 64 and 99520 divided by 64 is 1555. Therefore, B equals 1555.

Once again we have A and B and can get our answer to 99520 in its simplest radical form as follows:

√99520 = A√B

√99520 = 8√1555

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Simplify Square Root of 99521
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