Simplify Square Root of 84480

Here we will show you two methods that you can use to simplify the square root of 84480. In other words, we will show you how to find the square root of 84480 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.

√84480 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 84480 to simplify the square root of 84480. 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 84480. The factors of 84480 are 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 20, 22, 24, 30, 32, 33, 40, 44, 48, 55, 60, 64, 66, 80, 88, 96, 110, 120, 128, 132, 160, 165, 176, 192, 220, 240, 256, 264, 320, 330, 352, 384, 440, 480, 512, 528, 640, 660, 704, 768, 880, 960, 1056, 1280, 1320, 1408, 1536, 1760, 1920, 2112, 2560, 2640, 2816, 3520, 3840, 4224, 5280, 5632, 7040, 7680, 8448, 10560, 14080, 16896, 21120, 28160, 42240, and 84480. Furthermore, the greatest perfect square on this list is 256 and the square root of 256 is 16. Therefore, A equals 16.

B = Calculate 84480 divided by the greatest perfect square from the list of all factors of 84480. We determined above that the greatest perfect square from the list of all factors of 84480 is 256. Furthermore, 84480 divided by 256 is 330, therefore B equals 330.

Now we have A and B and can get our answer to 84480 in its simplest radical form as follows:

√84480 = A√B

√84480 = 16√330

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 84480 to simplify the square root of 84480 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 84480 and then take the square root of that product. The prime factors that multiply together to make 84480 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 11. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 256 and the square root of 256 is 16. Therefore, A equals 16.

B = Divide 84480 by the number (A) squared. 16 squared is 256 and 84480 divided by 256 is 330. Therefore, B equals 330.

Once again we have A and B and can get our answer to 84480 in its simplest radical form as follows:

√84480 = A√B

√84480 = 16√330

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

Simplify Square Root of 84481
Here is the next square root on our list that we have simplifed for you.