Simplify Square Root of 48375

Here we will show you two methods that you can use to simplify the square root of 48375. In other words, we will show you how to find the square root of 48375 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.

√48375 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 48375 to simplify the square root of 48375. 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 48375. The factors of 48375 are 1, 3, 5, 9, 15, 25, 43, 45, 75, 125, 129, 215, 225, 375, 387, 645, 1075, 1125, 1935, 3225, 5375, 9675, 16125, and 48375. Furthermore, the greatest perfect square on this list is 225 and the square root of 225 is 15. Therefore, A equals 15.

B = Calculate 48375 divided by the greatest perfect square from the list of all factors of 48375. We determined above that the greatest perfect square from the list of all factors of 48375 is 225. Furthermore, 48375 divided by 225 is 215, therefore B equals 215.

Now we have A and B and can get our answer to 48375 in its simplest radical form as follows:

√48375 = A√B

√48375 = 15√215

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 48375 to simplify the square root of 48375 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 48375 and then take the square root of that product. The prime factors that multiply together to make 48375 are 3 x 3 x 5 x 5 x 5 x 43. When we strip out the pairs only, we get 3 x 3 x 5 x 5 = 225 and the square root of 225 is 15. Therefore, A equals 15.

B = Divide 48375 by the number (A) squared. 15 squared is 225 and 48375 divided by 225 is 215. Therefore, B equals 215.

Once again we have A and B and can get our answer to 48375 in its simplest radical form as follows:

√48375 = A√B

√48375 = 15√215

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

Simplify Square Root of 48376
Here is the next square root on our list that we have simplifed for you.