Simplify Square Root of 66755

Here we will show you two methods that you can use to simplify the square root of 66755. In other words, we will show you how to find the square root of 66755 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.

√66755 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 66755 to simplify the square root of 66755. 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 66755. The factors of 66755 are 1, 5, 13, 65, 79, 169, 395, 845, 1027, 5135, 13351, and 66755. Furthermore, the greatest perfect square on this list is 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Calculate 66755 divided by the greatest perfect square from the list of all factors of 66755. We determined above that the greatest perfect square from the list of all factors of 66755 is 169. Furthermore, 66755 divided by 169 is 395, therefore B equals 395.

Now we have A and B and can get our answer to 66755 in its simplest radical form as follows:

√66755 = A√B

√66755 = 13√395

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 66755 to simplify the square root of 66755 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 66755 and then take the square root of that product. The prime factors that multiply together to make 66755 are 5 x 13 x 13 x 79. When we strip out the pairs only, we get 13 x 13 = 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Divide 66755 by the number (A) squared. 13 squared is 169 and 66755 divided by 169 is 395. Therefore, B equals 395.

Once again we have A and B and can get our answer to 66755 in its simplest radical form as follows:

√66755 = A√B

√66755 = 13√395

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

Simplify Square Root of 66756
Here is the next square root on our list that we have simplifed for you.