Simplify Square Root of 82800

Here we will show you two methods that you can use to simplify the square root of 82800. In other words, we will show you how to find the square root of 82800 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.

√82800 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 82800 to simplify the square root of 82800. 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 82800. The factors of 82800 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 23, 24, 25, 30, 36, 40, 45, 46, 48, 50, 60, 69, 72, 75, 80, 90, 92, 100, 115, 120, 138, 144, 150, 180, 184, 200, 207, 225, 230, 240, 276, 300, 345, 360, 368, 400, 414, 450, 460, 552, 575, 600, 690, 720, 828, 900, 920, 1035, 1104, 1150, 1200, 1380, 1656, 1725, 1800, 1840, 2070, 2300, 2760, 3312, 3450, 3600, 4140, 4600, 5175, 5520, 6900, 8280, 9200, 10350, 13800, 16560, 20700, 27600, 41400, and 82800. Furthermore, the greatest perfect square on this list is 3600 and the square root of 3600 is 60. Therefore, A equals 60.

B = Calculate 82800 divided by the greatest perfect square from the list of all factors of 82800. We determined above that the greatest perfect square from the list of all factors of 82800 is 3600. Furthermore, 82800 divided by 3600 is 23, therefore B equals 23.

Now we have A and B and can get our answer to 82800 in its simplest radical form as follows:

√82800 = A√B

√82800 = 60√23

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 82800 to simplify the square root of 82800 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 82800 and then take the square root of that product. The prime factors that multiply together to make 82800 are 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5 x 23. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5 = 3600 and the square root of 3600 is 60. Therefore, A equals 60.

B = Divide 82800 by the number (A) squared. 60 squared is 3600 and 82800 divided by 3600 is 23. Therefore, B equals 23.

Once again we have A and B and can get our answer to 82800 in its simplest radical form as follows:

√82800 = A√B

√82800 = 60√23

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