Simplify Square Root of 57375

Here we will show you two methods that you can use to simplify the square root of 57375. In other words, we will show you how to find the square root of 57375 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.

√57375 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 57375 to simplify the square root of 57375. 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 57375. The factors of 57375 are 1, 3, 5, 9, 15, 17, 25, 27, 45, 51, 75, 85, 125, 135, 153, 225, 255, 375, 425, 459, 675, 765, 1125, 1275, 2125, 2295, 3375, 3825, 6375, 11475, 19125, and 57375. Furthermore, the greatest perfect square on this list is 225 and the square root of 225 is 15. Therefore, A equals 15.

B = Calculate 57375 divided by the greatest perfect square from the list of all factors of 57375. We determined above that the greatest perfect square from the list of all factors of 57375 is 225. Furthermore, 57375 divided by 225 is 255, therefore B equals 255.

Now we have A and B and can get our answer to 57375 in its simplest radical form as follows:

√57375 = A√B

√57375 = 15√255

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 57375 to simplify the square root of 57375 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 57375 and then take the square root of that product. The prime factors that multiply together to make 57375 are 3 x 3 x 3 x 5 x 5 x 5 x 17. 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 57375 by the number (A) squared. 15 squared is 225 and 57375 divided by 225 is 255. Therefore, B equals 255.

Once again we have A and B and can get our answer to 57375 in its simplest radical form as follows:

√57375 = A√B

√57375 = 15√255

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

Simplify Square Root of 57376
Here is the next square root on our list that we have simplifed for you.