Simplify Square Root of 20808

Here we will show you two methods that you can use to simplify the square root of 20808. In other words, we will show you how to find the square root of 20808 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.

√20808 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 20808 to simplify the square root of 20808. 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 20808. The factors of 20808 are 1, 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 34, 36, 51, 68, 72, 102, 136, 153, 204, 289, 306, 408, 578, 612, 867, 1156, 1224, 1734, 2312, 2601, 3468, 5202, 6936, 10404, and 20808. Furthermore, the greatest perfect square on this list is 10404 and the square root of 10404 is 102. Therefore, A equals 102.

B = Calculate 20808 divided by the greatest perfect square from the list of all factors of 20808. We determined above that the greatest perfect square from the list of all factors of 20808 is 10404. Furthermore, 20808 divided by 10404 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 20808 in its simplest radical form as follows:

√20808 = A√B

√20808 = 102√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 20808 to simplify the square root of 20808 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 20808 and then take the square root of that product. The prime factors that multiply together to make 20808 are 2 x 2 x 2 x 3 x 3 x 17 x 17. When we strip out the pairs only, we get 2 x 2 x 3 x 3 x 17 x 17 = 10404 and the square root of 10404 is 102. Therefore, A equals 102.

B = Divide 20808 by the number (A) squared. 102 squared is 10404 and 20808 divided by 10404 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 20808 in its simplest radical form as follows:

√20808 = A√B

√20808 = 102√2

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

Simplify Square Root of 20809
Here is the next square root on our list that we have simplifed for you.