Simplify Square Root of 12960

Here we will show you two methods that you can use to simplify the square root of 12960. In other words, we will show you how to find the square root of 12960 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.

√12960 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 12960 to simplify the square root of 12960. 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 12960. The factors of 12960 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 32, 36, 40, 45, 48, 54, 60, 72, 80, 81, 90, 96, 108, 120, 135, 144, 160, 162, 180, 216, 240, 270, 288, 324, 360, 405, 432, 480, 540, 648, 720, 810, 864, 1080, 1296, 1440, 1620, 2160, 2592, 3240, 4320, 6480, and 12960. Furthermore, the greatest perfect square on this list is 1296 and the square root of 1296 is 36. Therefore, A equals 36.

B = Calculate 12960 divided by the greatest perfect square from the list of all factors of 12960. We determined above that the greatest perfect square from the list of all factors of 12960 is 1296. Furthermore, 12960 divided by 1296 is 10, therefore B equals 10.

Now we have A and B and can get our answer to 12960 in its simplest radical form as follows:

√12960 = A√B

√12960 = 36√10

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 12960 to simplify the square root of 12960 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 12960 and then take the square root of that product. The prime factors that multiply together to make 12960 are 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 5. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 = 1296 and the square root of 1296 is 36. Therefore, A equals 36.

B = Divide 12960 by the number (A) squared. 36 squared is 1296 and 12960 divided by 1296 is 10. Therefore, B equals 10.

Once again we have A and B and can get our answer to 12960 in its simplest radical form as follows:

√12960 = A√B

√12960 = 36√10

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Simplify Square Root of 12961
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