Simplify Square Root of 45927

Here we will show you two methods that you can use to simplify the square root of 45927. In other words, we will show you how to find the square root of 45927 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.

√45927 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 45927 to simplify the square root of 45927. 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 45927. The factors of 45927 are 1, 3, 7, 9, 21, 27, 63, 81, 189, 243, 567, 729, 1701, 2187, 5103, 6561, 15309, and 45927. Furthermore, the greatest perfect square on this list is 6561 and the square root of 6561 is 81. Therefore, A equals 81.

B = Calculate 45927 divided by the greatest perfect square from the list of all factors of 45927. We determined above that the greatest perfect square from the list of all factors of 45927 is 6561. Furthermore, 45927 divided by 6561 is 7, therefore B equals 7.

Now we have A and B and can get our answer to 45927 in its simplest radical form as follows:

√45927 = A√B

√45927 = 81√7

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 45927 to simplify the square root of 45927 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 45927 and then take the square root of that product. The prime factors that multiply together to make 45927 are 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 7. When we strip out the pairs only, we get 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 = 6561 and the square root of 6561 is 81. Therefore, A equals 81.

B = Divide 45927 by the number (A) squared. 81 squared is 6561 and 45927 divided by 6561 is 7. Therefore, B equals 7.

Once again we have A and B and can get our answer to 45927 in its simplest radical form as follows:

√45927 = A√B

√45927 = 81√7

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

Simplify Square Root of 45928
Here is the next square root on our list that we have simplifed for you.