Simplify Square Root of 208

Here we will show you two methods that you can use to simplify the square root of 208. In other words, we will show you how to find the square root of 208 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.

√208 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 208 to simplify the square root of 208. 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 208. The factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, and 208. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 208 divided by the greatest perfect square from the list of all factors of 208. We determined above that the greatest perfect square from the list of all factors of 208 is 16. Furthermore, 208 divided by 16 is 13, therefore B equals 13.

Now we have A and B and can get our answer to 208 in its simplest radical form as follows:

√208 = A√B

√208 = 4√13

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 208 to simplify the square root of 208 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 208 and then take the square root of that product. The prime factors that multiply together to make 208 are 2 x 2 x 2 x 2 x 13. 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 208 by the number (A) squared. 4 squared is 16 and 208 divided by 16 is 13. Therefore, B equals 13.

Once again we have A and B and can get our answer to 208 in its simplest radical form as follows:

√208 = A√B

√208 = 4√13

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

Simplify Square Root of 209
Here is the next square root on our list that we have simplifed for you.