Simplify Square Root of 82320

Here we will show you two methods that you can use to simplify the square root of 82320. In other words, we will show you how to find the square root of 82320 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.

√82320 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 82320 to simplify the square root of 82320. 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 82320. The factors of 82320 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 48, 49, 56, 60, 70, 80, 84, 98, 105, 112, 120, 140, 147, 168, 196, 210, 240, 245, 280, 294, 336, 343, 392, 420, 490, 560, 588, 686, 735, 784, 840, 980, 1029, 1176, 1372, 1470, 1680, 1715, 1960, 2058, 2352, 2744, 2940, 3430, 3920, 4116, 5145, 5488, 5880, 6860, 8232, 10290, 11760, 13720, 16464, 20580, 27440, 41160, and 82320. Furthermore, the greatest perfect square on this list is 784 and the square root of 784 is 28. Therefore, A equals 28.

B = Calculate 82320 divided by the greatest perfect square from the list of all factors of 82320. We determined above that the greatest perfect square from the list of all factors of 82320 is 784. Furthermore, 82320 divided by 784 is 105, therefore B equals 105.

Now we have A and B and can get our answer to 82320 in its simplest radical form as follows:

√82320 = A√B

√82320 = 28√105

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 82320 to simplify the square root of 82320 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 82320 and then take the square root of that product. The prime factors that multiply together to make 82320 are 2 x 2 x 2 x 2 x 3 x 5 x 7 x 7 x 7. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 7 x 7 = 784 and the square root of 784 is 28. Therefore, A equals 28.

B = Divide 82320 by the number (A) squared. 28 squared is 784 and 82320 divided by 784 is 105. Therefore, B equals 105.

Once again we have A and B and can get our answer to 82320 in its simplest radical form as follows:

√82320 = A√B

√82320 = 28√105

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

Simplify Square Root of 82321
Here is the next square root on our list that we have simplifed for you.