Simplify Square Root of 72116

Here we will show you two methods that you can use to simplify the square root of 72116. In other words, we will show you how to find the square root of 72116 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.

√72116 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 72116 to simplify the square root of 72116. 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 72116. The factors of 72116 are 1, 2, 4, 11, 22, 44, 121, 149, 242, 298, 484, 596, 1639, 3278, 6556, 18029, 36058, and 72116. Furthermore, the greatest perfect square on this list is 484 and the square root of 484 is 22. Therefore, A equals 22.

B = Calculate 72116 divided by the greatest perfect square from the list of all factors of 72116. We determined above that the greatest perfect square from the list of all factors of 72116 is 484. Furthermore, 72116 divided by 484 is 149, therefore B equals 149.

Now we have A and B and can get our answer to 72116 in its simplest radical form as follows:

√72116 = A√B

√72116 = 22√149

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 72116 to simplify the square root of 72116 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 72116 and then take the square root of that product. The prime factors that multiply together to make 72116 are 2 x 2 x 11 x 11 x 149. When we strip out the pairs only, we get 2 x 2 x 11 x 11 = 484 and the square root of 484 is 22. Therefore, A equals 22.

B = Divide 72116 by the number (A) squared. 22 squared is 484 and 72116 divided by 484 is 149. Therefore, B equals 149.

Once again we have A and B and can get our answer to 72116 in its simplest radical form as follows:

√72116 = A√B

√72116 = 22√149

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

Simplify Square Root of 72117
Here is the next square root on our list that we have simplifed for you.