Simplify Square Root of 768

Here we will show you two methods that you can use to simplify the square root of 768. In other words, we will show you how to find the square root of 768 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.

√768 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 768 to simplify the square root of 768. 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 768. The factors of 768 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, and 768. Furthermore, the greatest perfect square on this list is 256 and the square root of 256 is 16. Therefore, A equals 16.

B = Calculate 768 divided by the greatest perfect square from the list of all factors of 768. We determined above that the greatest perfect square from the list of all factors of 768 is 256. Furthermore, 768 divided by 256 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 768 in its simplest radical form as follows:

√768 = A√B

√768 = 16√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 768 to simplify the square root of 768 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 768 and then take the square root of that product. The prime factors that multiply together to make 768 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3. 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 768 by the number (A) squared. 16 squared is 256 and 768 divided by 256 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 768 in its simplest radical form as follows:

√768 = A√B

√768 = 16√3

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

Simplify Square Root of 769
Here is the next square root on our list that we have simplifed for you.