Simplify Square Root of 99416

Here we will show you two methods that you can use to simplify the square root of 99416. In other words, we will show you how to find the square root of 99416 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.

√99416 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 99416 to simplify the square root of 99416. 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 99416. The factors of 99416 are 1, 2, 4, 8, 17, 34, 43, 68, 86, 136, 172, 289, 344, 578, 731, 1156, 1462, 2312, 2924, 5848, 12427, 24854, 49708, and 99416. Furthermore, the greatest perfect square on this list is 1156 and the square root of 1156 is 34. Therefore, A equals 34.

B = Calculate 99416 divided by the greatest perfect square from the list of all factors of 99416. We determined above that the greatest perfect square from the list of all factors of 99416 is 1156. Furthermore, 99416 divided by 1156 is 86, therefore B equals 86.

Now we have A and B and can get our answer to 99416 in its simplest radical form as follows:

√99416 = A√B

√99416 = 34√86

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 99416 to simplify the square root of 99416 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 99416 and then take the square root of that product. The prime factors that multiply together to make 99416 are 2 x 2 x 2 x 17 x 17 x 43. When we strip out the pairs only, we get 2 x 2 x 17 x 17 = 1156 and the square root of 1156 is 34. Therefore, A equals 34.

B = Divide 99416 by the number (A) squared. 34 squared is 1156 and 99416 divided by 1156 is 86. Therefore, B equals 86.

Once again we have A and B and can get our answer to 99416 in its simplest radical form as follows:

√99416 = A√B

√99416 = 34√86

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