Simplify Square Root of 82467

Here we will show you two methods that you can use to simplify the square root of 82467. In other words, we will show you how to find the square root of 82467 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.

√82467 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 82467 to simplify the square root of 82467. 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 82467. The factors of 82467 are 1, 3, 7, 9, 11, 17, 21, 33, 49, 51, 63, 77, 99, 119, 147, 153, 187, 231, 357, 441, 539, 561, 693, 833, 1071, 1309, 1617, 1683, 2499, 3927, 4851, 7497, 9163, 11781, 27489, and 82467. Furthermore, the greatest perfect square on this list is 441 and the square root of 441 is 21. Therefore, A equals 21.

B = Calculate 82467 divided by the greatest perfect square from the list of all factors of 82467. We determined above that the greatest perfect square from the list of all factors of 82467 is 441. Furthermore, 82467 divided by 441 is 187, therefore B equals 187.

Now we have A and B and can get our answer to 82467 in its simplest radical form as follows:

√82467 = A√B

√82467 = 21√187

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 82467 to simplify the square root of 82467 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 82467 and then take the square root of that product. The prime factors that multiply together to make 82467 are 3 x 3 x 7 x 7 x 11 x 17. When we strip out the pairs only, we get 3 x 3 x 7 x 7 = 441 and the square root of 441 is 21. Therefore, A equals 21.

B = Divide 82467 by the number (A) squared. 21 squared is 441 and 82467 divided by 441 is 187. Therefore, B equals 187.

Once again we have A and B and can get our answer to 82467 in its simplest radical form as follows:

√82467 = A√B

√82467 = 21√187

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