Simplify Square Root of 72160

Here we will show you two methods that you can use to simplify the square root of 72160. In other words, we will show you how to find the square root of 72160 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.

√72160 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 72160 to simplify the square root of 72160. 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 72160. The factors of 72160 are 1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 32, 40, 41, 44, 55, 80, 82, 88, 110, 160, 164, 176, 205, 220, 328, 352, 410, 440, 451, 656, 820, 880, 902, 1312, 1640, 1760, 1804, 2255, 3280, 3608, 4510, 6560, 7216, 9020, 14432, 18040, 36080, and 72160. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 72160 divided by the greatest perfect square from the list of all factors of 72160. We determined above that the greatest perfect square from the list of all factors of 72160 is 16. Furthermore, 72160 divided by 16 is 4510, therefore B equals 4510.

Now we have A and B and can get our answer to 72160 in its simplest radical form as follows:

√72160 = A√B

√72160 = 4√4510

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 72160 to simplify the square root of 72160 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 72160 and then take the square root of that product. The prime factors that multiply together to make 72160 are 2 x 2 x 2 x 2 x 2 x 5 x 11 x 41. When we strip out the pairs only, we get 2 x 2 x 2 x 2 = 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Divide 72160 by the number (A) squared. 4 squared is 16 and 72160 divided by 16 is 4510. Therefore, B equals 4510.

Once again we have A and B and can get our answer to 72160 in its simplest radical form as follows:

√72160 = A√B

√72160 = 4√4510

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

Simplify Square Root of 72161
Here is the next square root on our list that we have simplifed for you.