Simplify Square Root of 20864

Here we will show you two methods that you can use to simplify the square root of 20864. In other words, we will show you how to find the square root of 20864 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.

√20864 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 20864 to simplify the square root of 20864. 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 20864. The factors of 20864 are 1, 2, 4, 8, 16, 32, 64, 128, 163, 326, 652, 1304, 2608, 5216, 10432, and 20864. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 20864 divided by the greatest perfect square from the list of all factors of 20864. We determined above that the greatest perfect square from the list of all factors of 20864 is 64. Furthermore, 20864 divided by 64 is 326, therefore B equals 326.

Now we have A and B and can get our answer to 20864 in its simplest radical form as follows:

√20864 = A√B

√20864 = 8√326

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 20864 to simplify the square root of 20864 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 20864 and then take the square root of that product. The prime factors that multiply together to make 20864 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 163. 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 20864 by the number (A) squared. 8 squared is 64 and 20864 divided by 64 is 326. Therefore, B equals 326.

Once again we have A and B and can get our answer to 20864 in its simplest radical form as follows:

√20864 = A√B

√20864 = 8√326

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

Simplify Square Root of 20865
Here is the next square root on our list that we have simplifed for you.