Simplify Square Root of 82522

Here we will show you two methods that you can use to simplify the square root of 82522. In other words, we will show you how to find the square root of 82522 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.

√82522 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 82522 to simplify the square root of 82522. 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 82522. The factors of 82522 are 1, 2, 11, 22, 31, 62, 121, 242, 341, 682, 1331, 2662, 3751, 7502, 41261, and 82522. Furthermore, the greatest perfect square on this list is 121 and the square root of 121 is 11. Therefore, A equals 11.

B = Calculate 82522 divided by the greatest perfect square from the list of all factors of 82522. We determined above that the greatest perfect square from the list of all factors of 82522 is 121. Furthermore, 82522 divided by 121 is 682, therefore B equals 682.

Now we have A and B and can get our answer to 82522 in its simplest radical form as follows:

√82522 = A√B

√82522 = 11√682

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 82522 to simplify the square root of 82522 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 82522 and then take the square root of that product. The prime factors that multiply together to make 82522 are 2 x 11 x 11 x 11 x 31. When we strip out the pairs only, we get 11 x 11 = 121 and the square root of 121 is 11. Therefore, A equals 11.

B = Divide 82522 by the number (A) squared. 11 squared is 121 and 82522 divided by 121 is 682. Therefore, B equals 682.

Once again we have A and B and can get our answer to 82522 in its simplest radical form as follows:

√82522 = A√B

√82522 = 11√682

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Simplify Square Root of 82523
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