Simplify Square Root of 82418

Here we will show you two methods that you can use to simplify the square root of 82418. In other words, we will show you how to find the square root of 82418 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.

√82418 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 82418 to simplify the square root of 82418. 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 82418. The factors of 82418 are 1, 2, 7, 14, 29, 49, 58, 98, 203, 406, 841, 1421, 1682, 2842, 5887, 11774, 41209, and 82418. Furthermore, the greatest perfect square on this list is 41209 and the square root of 41209 is 203. Therefore, A equals 203.

B = Calculate 82418 divided by the greatest perfect square from the list of all factors of 82418. We determined above that the greatest perfect square from the list of all factors of 82418 is 41209. Furthermore, 82418 divided by 41209 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 82418 in its simplest radical form as follows:

√82418 = A√B

√82418 = 203√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 82418 to simplify the square root of 82418 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 82418 and then take the square root of that product. The prime factors that multiply together to make 82418 are 2 x 7 x 7 x 29 x 29. When we strip out the pairs only, we get 7 x 7 x 29 x 29 = 41209 and the square root of 41209 is 203. Therefore, A equals 203.

B = Divide 82418 by the number (A) squared. 203 squared is 41209 and 82418 divided by 41209 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 82418 in its simplest radical form as follows:

√82418 = A√B

√82418 = 203√2

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