Simplify Square Root of 31833

Here we will show you two methods that you can use to simplify the square root of 31833. In other words, we will show you how to find the square root of 31833 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.

√31833 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 31833 to simplify the square root of 31833. 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 31833. The factors of 31833 are 1, 3, 9, 27, 81, 131, 243, 393, 1179, 3537, 10611, and 31833. Furthermore, the greatest perfect square on this list is 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Calculate 31833 divided by the greatest perfect square from the list of all factors of 31833. We determined above that the greatest perfect square from the list of all factors of 31833 is 81. Furthermore, 31833 divided by 81 is 393, therefore B equals 393.

Now we have A and B and can get our answer to 31833 in its simplest radical form as follows:

√31833 = A√B

√31833 = 9√393

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 31833 to simplify the square root of 31833 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 31833 and then take the square root of that product. The prime factors that multiply together to make 31833 are 3 x 3 x 3 x 3 x 3 x 131. When we strip out the pairs only, we get 3 x 3 x 3 x 3 = 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Divide 31833 by the number (A) squared. 9 squared is 81 and 31833 divided by 81 is 393. Therefore, B equals 393.

Once again we have A and B and can get our answer to 31833 in its simplest radical form as follows:

√31833 = A√B

√31833 = 9√393

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

Simplify Square Root of 31834
Here is the next square root on our list that we have simplifed for you.