Simplify Square Root of 81312

Here we will show you two methods that you can use to simplify the square root of 81312. In other words, we will show you how to find the square root of 81312 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.

√81312 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 81312 to simplify the square root of 81312. 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 81312. The factors of 81312 are 1, 2, 3, 4, 6, 7, 8, 11, 12, 14, 16, 21, 22, 24, 28, 32, 33, 42, 44, 48, 56, 66, 77, 84, 88, 96, 112, 121, 132, 154, 168, 176, 224, 231, 242, 264, 308, 336, 352, 363, 462, 484, 528, 616, 672, 726, 847, 924, 968, 1056, 1232, 1452, 1694, 1848, 1936, 2464, 2541, 2904, 3388, 3696, 3872, 5082, 5808, 6776, 7392, 10164, 11616, 13552, 20328, 27104, 40656, and 81312. Furthermore, the greatest perfect square on this list is 1936 and the square root of 1936 is 44. Therefore, A equals 44.

B = Calculate 81312 divided by the greatest perfect square from the list of all factors of 81312. We determined above that the greatest perfect square from the list of all factors of 81312 is 1936. Furthermore, 81312 divided by 1936 is 42, therefore B equals 42.

Now we have A and B and can get our answer to 81312 in its simplest radical form as follows:

√81312 = A√B

√81312 = 44√42

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 81312 to simplify the square root of 81312 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 81312 and then take the square root of that product. The prime factors that multiply together to make 81312 are 2 x 2 x 2 x 2 x 2 x 3 x 7 x 11 x 11. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 11 x 11 = 1936 and the square root of 1936 is 44. Therefore, A equals 44.

B = Divide 81312 by the number (A) squared. 44 squared is 1936 and 81312 divided by 1936 is 42. Therefore, B equals 42.

Once again we have A and B and can get our answer to 81312 in its simplest radical form as follows:

√81312 = A√B

√81312 = 44√42

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

Simplify Square Root of 81313
Here is the next square root on our list that we have simplifed for you.