Simplify Square Root of 9584

Here we will show you two methods that you can use to simplify the square root of 9584. In other words, we will show you how to find the square root of 9584 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.

√9584 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 9584 to simplify the square root of 9584. 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 9584. The factors of 9584 are 1, 2, 4, 8, 16, 599, 1198, 2396, 4792, and 9584. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 9584 divided by the greatest perfect square from the list of all factors of 9584. We determined above that the greatest perfect square from the list of all factors of 9584 is 16. Furthermore, 9584 divided by 16 is 599, therefore B equals 599.

Now we have A and B and can get our answer to 9584 in its simplest radical form as follows:

√9584 = A√B

√9584 = 4√599

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 9584 to simplify the square root of 9584 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 9584 and then take the square root of that product. The prime factors that multiply together to make 9584 are 2 x 2 x 2 x 2 x 599. When we strip out the pairs only, we get 2 x 2 x 2 x 2 = 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Divide 9584 by the number (A) squared. 4 squared is 16 and 9584 divided by 16 is 599. Therefore, B equals 599.

Once again we have A and B and can get our answer to 9584 in its simplest radical form as follows:

√9584 = A√B

√9584 = 4√599

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

Simplify Square Root of 9585
Here is the next square root on our list that we have simplifed for you.