Simplify Square Root of 99456

Here we will show you two methods that you can use to simplify the square root of 99456. In other words, we will show you how to find the square root of 99456 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.

√99456 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 99456 to simplify the square root of 99456. 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 99456. The factors of 99456 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 37, 42, 48, 56, 64, 74, 84, 96, 111, 112, 128, 148, 168, 192, 222, 224, 259, 296, 336, 384, 444, 448, 518, 592, 672, 777, 888, 896, 1036, 1184, 1344, 1554, 1776, 2072, 2368, 2688, 3108, 3552, 4144, 4736, 6216, 7104, 8288, 12432, 14208, 16576, 24864, 33152, 49728, and 99456. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 99456 divided by the greatest perfect square from the list of all factors of 99456. We determined above that the greatest perfect square from the list of all factors of 99456 is 64. Furthermore, 99456 divided by 64 is 1554, therefore B equals 1554.

Now we have A and B and can get our answer to 99456 in its simplest radical form as follows:

√99456 = A√B

√99456 = 8√1554

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 99456 to simplify the square root of 99456 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 99456 and then take the square root of that product. The prime factors that multiply together to make 99456 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 7 x 37. 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 99456 by the number (A) squared. 8 squared is 64 and 99456 divided by 64 is 1554. Therefore, B equals 1554.

Once again we have A and B and can get our answer to 99456 in its simplest radical form as follows:

√99456 = A√B

√99456 = 8√1554

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