Simplify Square Root of 53816

Here we will show you two methods that you can use to simplify the square root of 53816. In other words, we will show you how to find the square root of 53816 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.

√53816 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 53816 to simplify the square root of 53816. 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 53816. The factors of 53816 are 1, 2, 4, 7, 8, 14, 28, 31, 56, 62, 124, 217, 248, 434, 868, 961, 1736, 1922, 3844, 6727, 7688, 13454, 26908, and 53816. Furthermore, the greatest perfect square on this list is 3844 and the square root of 3844 is 62. Therefore, A equals 62.

B = Calculate 53816 divided by the greatest perfect square from the list of all factors of 53816. We determined above that the greatest perfect square from the list of all factors of 53816 is 3844. Furthermore, 53816 divided by 3844 is 14, therefore B equals 14.

Now we have A and B and can get our answer to 53816 in its simplest radical form as follows:

√53816 = A√B

√53816 = 62√14

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 53816 to simplify the square root of 53816 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 53816 and then take the square root of that product. The prime factors that multiply together to make 53816 are 2 x 2 x 2 x 7 x 31 x 31. When we strip out the pairs only, we get 2 x 2 x 31 x 31 = 3844 and the square root of 3844 is 62. Therefore, A equals 62.

B = Divide 53816 by the number (A) squared. 62 squared is 3844 and 53816 divided by 3844 is 14. Therefore, B equals 14.

Once again we have A and B and can get our answer to 53816 in its simplest radical form as follows:

√53816 = A√B

√53816 = 62√14

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

Simplify Square Root of 53817
Here is the next square root on our list that we have simplifed for you.