Simplify Square Root of 82064

Here we will show you two methods that you can use to simplify the square root of 82064. In other words, we will show you how to find the square root of 82064 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.

√82064 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 82064 to simplify the square root of 82064. 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 82064. The factors of 82064 are 1, 2, 4, 8, 16, 23, 46, 92, 184, 223, 368, 446, 892, 1784, 3568, 5129, 10258, 20516, 41032, and 82064. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 82064 divided by the greatest perfect square from the list of all factors of 82064. We determined above that the greatest perfect square from the list of all factors of 82064 is 16. Furthermore, 82064 divided by 16 is 5129, therefore B equals 5129.

Now we have A and B and can get our answer to 82064 in its simplest radical form as follows:

√82064 = A√B

√82064 = 4√5129

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 82064 to simplify the square root of 82064 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 82064 and then take the square root of that product. The prime factors that multiply together to make 82064 are 2 x 2 x 2 x 2 x 23 x 223. 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 82064 by the number (A) squared. 4 squared is 16 and 82064 divided by 16 is 5129. Therefore, B equals 5129.

Once again we have A and B and can get our answer to 82064 in its simplest radical form as follows:

√82064 = A√B

√82064 = 4√5129

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

Simplify Square Root of 82065
Here is the next square root on our list that we have simplifed for you.