Simplify Square Root of 53872

Here we will show you two methods that you can use to simplify the square root of 53872. In other words, we will show you how to find the square root of 53872 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.

√53872 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 53872 to simplify the square root of 53872. 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 53872. The factors of 53872 are 1, 2, 4, 7, 8, 13, 14, 16, 26, 28, 37, 52, 56, 74, 91, 104, 112, 148, 182, 208, 259, 296, 364, 481, 518, 592, 728, 962, 1036, 1456, 1924, 2072, 3367, 3848, 4144, 6734, 7696, 13468, 26936, and 53872. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 53872 divided by the greatest perfect square from the list of all factors of 53872. We determined above that the greatest perfect square from the list of all factors of 53872 is 16. Furthermore, 53872 divided by 16 is 3367, therefore B equals 3367.

Now we have A and B and can get our answer to 53872 in its simplest radical form as follows:

√53872 = A√B

√53872 = 4√3367

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 53872 to simplify the square root of 53872 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 53872 and then take the square root of that product. The prime factors that multiply together to make 53872 are 2 x 2 x 2 x 2 x 7 x 13 x 37. When we strip out the pairs only, we get 2 x 2 x 2 x 2 = 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Divide 53872 by the number (A) squared. 4 squared is 16 and 53872 divided by 16 is 3367. Therefore, B equals 3367.

Once again we have A and B and can get our answer to 53872 in its simplest radical form as follows:

√53872 = A√B

√53872 = 4√3367

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

Simplify Square Root of 53873
Here is the next square root on our list that we have simplifed for you.