Simplify Square Root of 82303

Here we will show you two methods that you can use to simplify the square root of 82303. In other words, we will show you how to find the square root of 82303 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.

√82303 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 82303 to simplify the square root of 82303. 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 82303. The factors of 82303 are 1, 13, 169, 487, 6331, and 82303. Furthermore, the greatest perfect square on this list is 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Calculate 82303 divided by the greatest perfect square from the list of all factors of 82303. We determined above that the greatest perfect square from the list of all factors of 82303 is 169. Furthermore, 82303 divided by 169 is 487, therefore B equals 487.

Now we have A and B and can get our answer to 82303 in its simplest radical form as follows:

√82303 = A√B

√82303 = 13√487

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 82303 to simplify the square root of 82303 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 82303 and then take the square root of that product. The prime factors that multiply together to make 82303 are 13 x 13 x 487. When we strip out the pairs only, we get 13 x 13 = 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Divide 82303 by the number (A) squared. 13 squared is 169 and 82303 divided by 169 is 487. Therefore, B equals 487.

Once again we have A and B and can get our answer to 82303 in its simplest radical form as follows:

√82303 = A√B

√82303 = 13√487

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

Simplify Square Root of 82304
Here is the next square root on our list that we have simplifed for you.