Simplify Square Root of 17125

Here we will show you two methods that you can use to simplify the square root of 17125. In other words, we will show you how to find the square root of 17125 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.

√17125 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 17125 to simplify the square root of 17125. 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 17125. The factors of 17125 are 1, 5, 25, 125, 137, 685, 3425, and 17125. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 17125 divided by the greatest perfect square from the list of all factors of 17125. We determined above that the greatest perfect square from the list of all factors of 17125 is 25. Furthermore, 17125 divided by 25 is 685, therefore B equals 685.

Now we have A and B and can get our answer to 17125 in its simplest radical form as follows:

√17125 = A√B

√17125 = 5√685

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 17125 to simplify the square root of 17125 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 17125 and then take the square root of that product. The prime factors that multiply together to make 17125 are 5 x 5 x 5 x 137. 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 17125 by the number (A) squared. 5 squared is 25 and 17125 divided by 25 is 685. Therefore, B equals 685.

Once again we have A and B and can get our answer to 17125 in its simplest radical form as follows:

√17125 = A√B

√17125 = 5√685

Simplify Square Root
Please enter another square root in the box below for us to simplify.

Simplify Square Root of 17126
Here is the next square root on our list that we have simplifed for you.