Simplify Square Root of 30375

Here we will show you two methods that you can use to simplify the square root of 30375. In other words, we will show you how to find the square root of 30375 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.

√30375 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 30375 to simplify the square root of 30375. 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 30375. The factors of 30375 are 1, 3, 5, 9, 15, 25, 27, 45, 75, 81, 125, 135, 225, 243, 375, 405, 675, 1125, 1215, 2025, 3375, 6075, 10125, and 30375. Furthermore, the greatest perfect square on this list is 2025 and the square root of 2025 is 45. Therefore, A equals 45.

B = Calculate 30375 divided by the greatest perfect square from the list of all factors of 30375. We determined above that the greatest perfect square from the list of all factors of 30375 is 2025. Furthermore, 30375 divided by 2025 is 15, therefore B equals 15.

Now we have A and B and can get our answer to 30375 in its simplest radical form as follows:

√30375 = A√B

√30375 = 45√15

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 30375 to simplify the square root of 30375 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 30375 and then take the square root of that product. The prime factors that multiply together to make 30375 are 3 x 3 x 3 x 3 x 3 x 5 x 5 x 5. When we strip out the pairs only, we get 3 x 3 x 3 x 3 x 5 x 5 = 2025 and the square root of 2025 is 45. Therefore, A equals 45.

B = Divide 30375 by the number (A) squared. 45 squared is 2025 and 30375 divided by 2025 is 15. Therefore, B equals 15.

Once again we have A and B and can get our answer to 30375 in its simplest radical form as follows:

√30375 = A√B

√30375 = 45√15

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

Simplify Square Root of 30376
Here is the next square root on our list that we have simplifed for you.