Simplify Square Root of 99704

Here we will show you two methods that you can use to simplify the square root of 99704. In other words, we will show you how to find the square root of 99704 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.

√99704 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 99704 to simplify the square root of 99704. 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 99704. The factors of 99704 are 1, 2, 4, 8, 11, 22, 44, 88, 103, 121, 206, 242, 412, 484, 824, 968, 1133, 2266, 4532, 9064, 12463, 24926, 49852, and 99704. Furthermore, the greatest perfect square on this list is 484 and the square root of 484 is 22. Therefore, A equals 22.

B = Calculate 99704 divided by the greatest perfect square from the list of all factors of 99704. We determined above that the greatest perfect square from the list of all factors of 99704 is 484. Furthermore, 99704 divided by 484 is 206, therefore B equals 206.

Now we have A and B and can get our answer to 99704 in its simplest radical form as follows:

√99704 = A√B

√99704 = 22√206

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 99704 to simplify the square root of 99704 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 99704 and then take the square root of that product. The prime factors that multiply together to make 99704 are 2 x 2 x 2 x 11 x 11 x 103. When we strip out the pairs only, we get 2 x 2 x 11 x 11 = 484 and the square root of 484 is 22. Therefore, A equals 22.

B = Divide 99704 by the number (A) squared. 22 squared is 484 and 99704 divided by 484 is 206. Therefore, B equals 206.

Once again we have A and B and can get our answer to 99704 in its simplest radical form as follows:

√99704 = A√B

√99704 = 22√206

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