Simplify Square Root of 93125

Here we will show you two methods that you can use to simplify the square root of 93125. In other words, we will show you how to find the square root of 93125 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.

√93125 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 93125 to simplify the square root of 93125. 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 93125. The factors of 93125 are 1, 5, 25, 125, 149, 625, 745, 3725, 18625, and 93125. Furthermore, the greatest perfect square on this list is 625 and the square root of 625 is 25. Therefore, A equals 25.

B = Calculate 93125 divided by the greatest perfect square from the list of all factors of 93125. We determined above that the greatest perfect square from the list of all factors of 93125 is 625. Furthermore, 93125 divided by 625 is 149, therefore B equals 149.

Now we have A and B and can get our answer to 93125 in its simplest radical form as follows:

√93125 = A√B

√93125 = 25√149

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 93125 to simplify the square root of 93125 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 93125 and then take the square root of that product. The prime factors that multiply together to make 93125 are 5 x 5 x 5 x 5 x 149. When we strip out the pairs only, we get 5 x 5 x 5 x 5 = 625 and the square root of 625 is 25. Therefore, A equals 25.

B = Divide 93125 by the number (A) squared. 25 squared is 625 and 93125 divided by 625 is 149. Therefore, B equals 149.

Once again we have A and B and can get our answer to 93125 in its simplest radical form as follows:

√93125 = A√B

√93125 = 25√149

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Simplify Square Root of 93126
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