Simplify Square Root of 99125

Here we will show you two methods that you can use to simplify the square root of 99125. In other words, we will show you how to find the square root of 99125 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.

√99125 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 99125 to simplify the square root of 99125. 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 99125. The factors of 99125 are 1, 5, 13, 25, 61, 65, 125, 305, 325, 793, 1525, 1625, 3965, 7625, 19825, and 99125. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 99125 divided by the greatest perfect square from the list of all factors of 99125. We determined above that the greatest perfect square from the list of all factors of 99125 is 25. Furthermore, 99125 divided by 25 is 3965, therefore B equals 3965.

Now we have A and B and can get our answer to 99125 in its simplest radical form as follows:

√99125 = A√B

√99125 = 5√3965

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 99125 to simplify the square root of 99125 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 99125 and then take the square root of that product. The prime factors that multiply together to make 99125 are 5 x 5 x 5 x 13 x 61. When we strip out the pairs only, we get 5 x 5 = 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Divide 99125 by the number (A) squared. 5 squared is 25 and 99125 divided by 25 is 3965. Therefore, B equals 3965.

Once again we have A and B and can get our answer to 99125 in its simplest radical form as follows:

√99125 = A√B

√99125 = 5√3965

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Simplify Square Root of 99126
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