Simplify Square Root of 83520

Here we will show you two methods that you can use to simplify the square root of 83520. In other words, we will show you how to find the square root of 83520 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.

√83520 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 83520 to simplify the square root of 83520. 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 83520. The factors of 83520 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 29, 30, 32, 36, 40, 45, 48, 58, 60, 64, 72, 80, 87, 90, 96, 116, 120, 144, 145, 160, 174, 180, 192, 232, 240, 261, 288, 290, 320, 348, 360, 435, 464, 480, 522, 576, 580, 696, 720, 870, 928, 960, 1044, 1160, 1305, 1392, 1440, 1740, 1856, 2088, 2320, 2610, 2784, 2880, 3480, 4176, 4640, 5220, 5568, 6960, 8352, 9280, 10440, 13920, 16704, 20880, 27840, 41760, and 83520. Furthermore, the greatest perfect square on this list is 576 and the square root of 576 is 24. Therefore, A equals 24.

B = Calculate 83520 divided by the greatest perfect square from the list of all factors of 83520. We determined above that the greatest perfect square from the list of all factors of 83520 is 576. Furthermore, 83520 divided by 576 is 145, therefore B equals 145.

Now we have A and B and can get our answer to 83520 in its simplest radical form as follows:

√83520 = A√B

√83520 = 24√145

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 83520 to simplify the square root of 83520 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 83520 and then take the square root of that product. The prime factors that multiply together to make 83520 are 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 29. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 = 576 and the square root of 576 is 24. Therefore, A equals 24.

B = Divide 83520 by the number (A) squared. 24 squared is 576 and 83520 divided by 576 is 145. Therefore, B equals 145.

Once again we have A and B and can get our answer to 83520 in its simplest radical form as follows:

√83520 = A√B

√83520 = 24√145

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

Simplify Square Root of 83521
Here is the next square root on our list that we have simplifed for you.