Simplify Square Root of 82396

Here we will show you two methods that you can use to simplify the square root of 82396. In other words, we will show you how to find the square root of 82396 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.

√82396 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 82396 to simplify the square root of 82396. 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 82396. The factors of 82396 are 1, 2, 4, 20599, 41198, and 82396. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 82396 divided by the greatest perfect square from the list of all factors of 82396. We determined above that the greatest perfect square from the list of all factors of 82396 is 4. Furthermore, 82396 divided by 4 is 20599, therefore B equals 20599.

Now we have A and B and can get our answer to 82396 in its simplest radical form as follows:

√82396 = A√B

√82396 = 2√20599

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 82396 to simplify the square root of 82396 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 82396 and then take the square root of that product. The prime factors that multiply together to make 82396 are 2 x 2 x 20599. When we strip out the pairs only, we get 2 x 2 = 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Divide 82396 by the number (A) squared. 2 squared is 4 and 82396 divided by 4 is 20599. Therefore, B equals 20599.

Once again we have A and B and can get our answer to 82396 in its simplest radical form as follows:

√82396 = A√B

√82396 = 2√20599

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

Simplify Square Root of 82397
Here is the next square root on our list that we have simplifed for you.