Simplify Square Root of 896

Here we will show you two methods that you can use to simplify the square root of 896. In other words, we will show you how to find the square root of 896 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.

√896 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 896 to simplify the square root of 896. 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 896. The factors of 896 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 448, and 896. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 896 divided by the greatest perfect square from the list of all factors of 896. We determined above that the greatest perfect square from the list of all factors of 896 is 64. Furthermore, 896 divided by 64 is 14, therefore B equals 14.

Now we have A and B and can get our answer to 896 in its simplest radical form as follows:

√896 = A√B

√896 = 8√14

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 896 to simplify the square root of 896 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 896 and then take the square root of that product. The prime factors that multiply together to make 896 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 7. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 = 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Divide 896 by the number (A) squared. 8 squared is 64 and 896 divided by 64 is 14. Therefore, B equals 14.

Once again we have A and B and can get our answer to 896 in its simplest radical form as follows:

√896 = A√B

√896 = 8√14

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

Simplify Square Root of 897
Here is the next square root on our list that we have simplifed for you.