Simplify Square Root of 82600

Here we will show you two methods that you can use to simplify the square root of 82600. In other words, we will show you how to find the square root of 82600 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.

√82600 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 82600 to simplify the square root of 82600. 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 82600. The factors of 82600 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 59, 70, 100, 118, 140, 175, 200, 236, 280, 295, 350, 413, 472, 590, 700, 826, 1180, 1400, 1475, 1652, 2065, 2360, 2950, 3304, 4130, 5900, 8260, 10325, 11800, 16520, 20650, 41300, and 82600. Furthermore, the greatest perfect square on this list is 100 and the square root of 100 is 10. Therefore, A equals 10.

B = Calculate 82600 divided by the greatest perfect square from the list of all factors of 82600. We determined above that the greatest perfect square from the list of all factors of 82600 is 100. Furthermore, 82600 divided by 100 is 826, therefore B equals 826.

Now we have A and B and can get our answer to 82600 in its simplest radical form as follows:

√82600 = A√B

√82600 = 10√826

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 82600 to simplify the square root of 82600 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 82600 and then take the square root of that product. The prime factors that multiply together to make 82600 are 2 x 2 x 2 x 5 x 5 x 7 x 59. When we strip out the pairs only, we get 2 x 2 x 5 x 5 = 100 and the square root of 100 is 10. Therefore, A equals 10.

B = Divide 82600 by the number (A) squared. 10 squared is 100 and 82600 divided by 100 is 826. Therefore, B equals 826.

Once again we have A and B and can get our answer to 82600 in its simplest radical form as follows:

√82600 = A√B

√82600 = 10√826

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