Simplify Square Root of 82472

Here we will show you two methods that you can use to simplify the square root of 82472. In other words, we will show you how to find the square root of 82472 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.

√82472 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 82472 to simplify the square root of 82472. 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 82472. The factors of 82472 are 1, 2, 4, 8, 13, 26, 52, 61, 104, 122, 169, 244, 338, 488, 676, 793, 1352, 1586, 3172, 6344, 10309, 20618, 41236, and 82472. Furthermore, the greatest perfect square on this list is 676 and the square root of 676 is 26. Therefore, A equals 26.

B = Calculate 82472 divided by the greatest perfect square from the list of all factors of 82472. We determined above that the greatest perfect square from the list of all factors of 82472 is 676. Furthermore, 82472 divided by 676 is 122, therefore B equals 122.

Now we have A and B and can get our answer to 82472 in its simplest radical form as follows:

√82472 = A√B

√82472 = 26√122

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 82472 to simplify the square root of 82472 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 82472 and then take the square root of that product. The prime factors that multiply together to make 82472 are 2 x 2 x 2 x 13 x 13 x 61. When we strip out the pairs only, we get 2 x 2 x 13 x 13 = 676 and the square root of 676 is 26. Therefore, A equals 26.

B = Divide 82472 by the number (A) squared. 26 squared is 676 and 82472 divided by 676 is 122. Therefore, B equals 122.

Once again we have A and B and can get our answer to 82472 in its simplest radical form as follows:

√82472 = A√B

√82472 = 26√122

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