Simplify Square Root of 85600

Here we will show you two methods that you can use to simplify the square root of 85600. In other words, we will show you how to find the square root of 85600 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.

√85600 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 85600 to simplify the square root of 85600. 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 85600. The factors of 85600 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 107, 160, 200, 214, 400, 428, 535, 800, 856, 1070, 1712, 2140, 2675, 3424, 4280, 5350, 8560, 10700, 17120, 21400, 42800, and 85600. Furthermore, the greatest perfect square on this list is 400 and the square root of 400 is 20. Therefore, A equals 20.

B = Calculate 85600 divided by the greatest perfect square from the list of all factors of 85600. We determined above that the greatest perfect square from the list of all factors of 85600 is 400. Furthermore, 85600 divided by 400 is 214, therefore B equals 214.

Now we have A and B and can get our answer to 85600 in its simplest radical form as follows:

√85600 = A√B

√85600 = 20√214

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 85600 to simplify the square root of 85600 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 85600 and then take the square root of that product. The prime factors that multiply together to make 85600 are 2 x 2 x 2 x 2 x 2 x 5 x 5 x 107. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 5 x 5 = 400 and the square root of 400 is 20. Therefore, A equals 20.

B = Divide 85600 by the number (A) squared. 20 squared is 400 and 85600 divided by 400 is 214. Therefore, B equals 214.

Once again we have A and B and can get our answer to 85600 in its simplest radical form as follows:

√85600 = A√B

√85600 = 20√214

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

Simplify Square Root of 85601
Here is the next square root on our list that we have simplifed for you.