Simplify Square Root of 53760

Here we will show you two methods that you can use to simplify the square root of 53760. In other words, we will show you how to find the square root of 53760 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.

√53760 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 53760 to simplify the square root of 53760. 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 53760. The factors of 53760 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 32, 35, 40, 42, 48, 56, 60, 64, 70, 80, 84, 96, 105, 112, 120, 128, 140, 160, 168, 192, 210, 224, 240, 256, 280, 320, 336, 384, 420, 448, 480, 512, 560, 640, 672, 768, 840, 896, 960, 1120, 1280, 1344, 1536, 1680, 1792, 1920, 2240, 2560, 2688, 3360, 3584, 3840, 4480, 5376, 6720, 7680, 8960, 10752, 13440, 17920, 26880, and 53760. Furthermore, the greatest perfect square on this list is 256 and the square root of 256 is 16. Therefore, A equals 16.

B = Calculate 53760 divided by the greatest perfect square from the list of all factors of 53760. We determined above that the greatest perfect square from the list of all factors of 53760 is 256. Furthermore, 53760 divided by 256 is 210, therefore B equals 210.

Now we have A and B and can get our answer to 53760 in its simplest radical form as follows:

√53760 = A√B

√53760 = 16√210

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 53760 to simplify the square root of 53760 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 53760 and then take the square root of that product. The prime factors that multiply together to make 53760 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 7. 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 53760 by the number (A) squared. 16 squared is 256 and 53760 divided by 256 is 210. Therefore, B equals 210.

Once again we have A and B and can get our answer to 53760 in its simplest radical form as follows:

√53760 = A√B

√53760 = 16√210

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

Simplify Square Root of 53761
Here is the next square root on our list that we have simplifed for you.