Simplify Square Root of 82810

Here we will show you two methods that you can use to simplify the square root of 82810. In other words, we will show you how to find the square root of 82810 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.

√82810 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 82810 to simplify the square root of 82810. 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 82810. The factors of 82810 are 1, 2, 5, 7, 10, 13, 14, 26, 35, 49, 65, 70, 91, 98, 130, 169, 182, 245, 338, 455, 490, 637, 845, 910, 1183, 1274, 1690, 2366, 3185, 5915, 6370, 8281, 11830, 16562, 41405, and 82810. Furthermore, the greatest perfect square on this list is 8281 and the square root of 8281 is 91. Therefore, A equals 91.

B = Calculate 82810 divided by the greatest perfect square from the list of all factors of 82810. We determined above that the greatest perfect square from the list of all factors of 82810 is 8281. Furthermore, 82810 divided by 8281 is 10, therefore B equals 10.

Now we have A and B and can get our answer to 82810 in its simplest radical form as follows:

√82810 = A√B

√82810 = 91√10

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 82810 to simplify the square root of 82810 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 82810 and then take the square root of that product. The prime factors that multiply together to make 82810 are 2 x 5 x 7 x 7 x 13 x 13. When we strip out the pairs only, we get 7 x 7 x 13 x 13 = 8281 and the square root of 8281 is 91. Therefore, A equals 91.

B = Divide 82810 by the number (A) squared. 91 squared is 8281 and 82810 divided by 8281 is 10. Therefore, B equals 10.

Once again we have A and B and can get our answer to 82810 in its simplest radical form as follows:

√82810 = A√B

√82810 = 91√10

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