Simplify Square Root of 16125

Here we will show you two methods that you can use to simplify the square root of 16125. In other words, we will show you how to find the square root of 16125 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.

√16125 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 16125 to simplify the square root of 16125. 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 16125. The factors of 16125 are 1, 3, 5, 15, 25, 43, 75, 125, 129, 215, 375, 645, 1075, 3225, 5375, and 16125. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 16125 divided by the greatest perfect square from the list of all factors of 16125. We determined above that the greatest perfect square from the list of all factors of 16125 is 25. Furthermore, 16125 divided by 25 is 645, therefore B equals 645.

Now we have A and B and can get our answer to 16125 in its simplest radical form as follows:

√16125 = A√B

√16125 = 5√645

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 16125 to simplify the square root of 16125 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 16125 and then take the square root of that product. The prime factors that multiply together to make 16125 are 3 x 5 x 5 x 5 x 43. 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 16125 by the number (A) squared. 5 squared is 25 and 16125 divided by 25 is 645. Therefore, B equals 645.

Once again we have A and B and can get our answer to 16125 in its simplest radical form as follows:

√16125 = A√B

√16125 = 5√645

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

Simplify Square Root of 16126
Here is the next square root on our list that we have simplifed for you.