Simplify Square Root of 82584

Here we will show you two methods that you can use to simplify the square root of 82584. In other words, we will show you how to find the square root of 82584 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.

√82584 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 82584 to simplify the square root of 82584. 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 82584. The factors of 82584 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 31, 36, 37, 62, 72, 74, 93, 111, 124, 148, 186, 222, 248, 279, 296, 333, 372, 444, 558, 666, 744, 888, 1116, 1147, 1332, 2232, 2294, 2664, 3441, 4588, 6882, 9176, 10323, 13764, 20646, 27528, 41292, and 82584. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 82584 divided by the greatest perfect square from the list of all factors of 82584. We determined above that the greatest perfect square from the list of all factors of 82584 is 36. Furthermore, 82584 divided by 36 is 2294, therefore B equals 2294.

Now we have A and B and can get our answer to 82584 in its simplest radical form as follows:

√82584 = A√B

√82584 = 6√2294

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 82584 to simplify the square root of 82584 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 82584 and then take the square root of that product. The prime factors that multiply together to make 82584 are 2 x 2 x 2 x 3 x 3 x 31 x 37. When we strip out the pairs only, we get 2 x 2 x 3 x 3 = 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Divide 82584 by the number (A) squared. 6 squared is 36 and 82584 divided by 36 is 2294. Therefore, B equals 2294.

Once again we have A and B and can get our answer to 82584 in its simplest radical form as follows:

√82584 = A√B

√82584 = 6√2294

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

Simplify Square Root of 82585
Here is the next square root on our list that we have simplifed for you.