Simplify Square Root of 82161

Here we will show you two methods that you can use to simplify the square root of 82161. In other words, we will show you how to find the square root of 82161 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.

√82161 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 82161 to simplify the square root of 82161. 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 82161. The factors of 82161 are 1, 3, 9, 17, 27, 51, 153, 179, 459, 537, 1611, 3043, 4833, 9129, 27387, and 82161. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 82161 divided by the greatest perfect square from the list of all factors of 82161. We determined above that the greatest perfect square from the list of all factors of 82161 is 9. Furthermore, 82161 divided by 9 is 9129, therefore B equals 9129.

Now we have A and B and can get our answer to 82161 in its simplest radical form as follows:

√82161 = A√B

√82161 = 3√9129

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 82161 to simplify the square root of 82161 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 82161 and then take the square root of that product. The prime factors that multiply together to make 82161 are 3 x 3 x 3 x 17 x 179. When we strip out the pairs only, we get 3 x 3 = 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Divide 82161 by the number (A) squared. 3 squared is 9 and 82161 divided by 9 is 9129. Therefore, B equals 9129.

Once again we have A and B and can get our answer to 82161 in its simplest radical form as follows:

√82161 = A√B

√82161 = 3√9129

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

Simplify Square Root of 82162
Here is the next square root on our list that we have simplifed for you.