Simplify Square Root of 56016

Here we will show you two methods that you can use to simplify the square root of 56016. In other words, we will show you how to find the square root of 56016 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.

√56016 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 56016 to simplify the square root of 56016. 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 56016. The factors of 56016 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 389, 778, 1167, 1556, 2334, 3112, 3501, 4668, 6224, 7002, 9336, 14004, 18672, 28008, and 56016. Furthermore, the greatest perfect square on this list is 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Calculate 56016 divided by the greatest perfect square from the list of all factors of 56016. We determined above that the greatest perfect square from the list of all factors of 56016 is 144. Furthermore, 56016 divided by 144 is 389, therefore B equals 389.

Now we have A and B and can get our answer to 56016 in its simplest radical form as follows:

√56016 = A√B

√56016 = 12√389

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 56016 to simplify the square root of 56016 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 56016 and then take the square root of that product. The prime factors that multiply together to make 56016 are 2 x 2 x 2 x 2 x 3 x 3 x 389. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 3 x 3 = 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Divide 56016 by the number (A) squared. 12 squared is 144 and 56016 divided by 144 is 389. Therefore, B equals 389.

Once again we have A and B and can get our answer to 56016 in its simplest radical form as follows:

√56016 = A√B

√56016 = 12√389

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

Simplify Square Root of 56017
Here is the next square root on our list that we have simplifed for you.