Simplify Square Root of 85920

Here we will show you two methods that you can use to simplify the square root of 85920. In other words, we will show you how to find the square root of 85920 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.

√85920 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 85920 to simplify the square root of 85920. 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 85920. The factors of 85920 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 179, 240, 358, 480, 537, 716, 895, 1074, 1432, 1790, 2148, 2685, 2864, 3580, 4296, 5370, 5728, 7160, 8592, 10740, 14320, 17184, 21480, 28640, 42960, and 85920. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 85920 divided by the greatest perfect square from the list of all factors of 85920. We determined above that the greatest perfect square from the list of all factors of 85920 is 16. Furthermore, 85920 divided by 16 is 5370, therefore B equals 5370.

Now we have A and B and can get our answer to 85920 in its simplest radical form as follows:

√85920 = A√B

√85920 = 4√5370

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 85920 to simplify the square root of 85920 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 85920 and then take the square root of that product. The prime factors that multiply together to make 85920 are 2 x 2 x 2 x 2 x 2 x 3 x 5 x 179. 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 85920 by the number (A) squared. 4 squared is 16 and 85920 divided by 16 is 5370. Therefore, B equals 5370.

Once again we have A and B and can get our answer to 85920 in its simplest radical form as follows:

√85920 = A√B

√85920 = 4√5370

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

Simplify Square Root of 85921
Here is the next square root on our list that we have simplifed for you.