Simplify Square Root of 82646

Here we will show you two methods that you can use to simplify the square root of 82646. In other words, we will show you how to find the square root of 82646 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.

√82646 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 82646 to simplify the square root of 82646. 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 82646. The factors of 82646 are 1, 2, 31, 43, 62, 86, 961, 1333, 1922, 2666, 41323, and 82646. Furthermore, the greatest perfect square on this list is 961 and the square root of 961 is 31. Therefore, A equals 31.

B = Calculate 82646 divided by the greatest perfect square from the list of all factors of 82646. We determined above that the greatest perfect square from the list of all factors of 82646 is 961. Furthermore, 82646 divided by 961 is 86, therefore B equals 86.

Now we have A and B and can get our answer to 82646 in its simplest radical form as follows:

√82646 = A√B

√82646 = 31√86

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 82646 to simplify the square root of 82646 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 82646 and then take the square root of that product. The prime factors that multiply together to make 82646 are 2 x 31 x 31 x 43. When we strip out the pairs only, we get 31 x 31 = 961 and the square root of 961 is 31. Therefore, A equals 31.

B = Divide 82646 by the number (A) squared. 31 squared is 961 and 82646 divided by 961 is 86. Therefore, B equals 86.

Once again we have A and B and can get our answer to 82646 in its simplest radical form as follows:

√82646 = A√B

√82646 = 31√86

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Simplify Square Root of 82647
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