Simplify Square Root of 12240

Here we will show you two methods that you can use to simplify the square root of 12240. In other words, we will show you how to find the square root of 12240 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.

√12240 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 12240 to simplify the square root of 12240. 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 12240. The factors of 12240 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 17, 18, 20, 24, 30, 34, 36, 40, 45, 48, 51, 60, 68, 72, 80, 85, 90, 102, 120, 136, 144, 153, 170, 180, 204, 240, 255, 272, 306, 340, 360, 408, 510, 612, 680, 720, 765, 816, 1020, 1224, 1360, 1530, 2040, 2448, 3060, 4080, 6120, and 12240. Furthermore, the greatest perfect square on this list is 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Calculate 12240 divided by the greatest perfect square from the list of all factors of 12240. We determined above that the greatest perfect square from the list of all factors of 12240 is 144. Furthermore, 12240 divided by 144 is 85, therefore B equals 85.

Now we have A and B and can get our answer to 12240 in its simplest radical form as follows:

√12240 = A√B

√12240 = 12√85

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 12240 to simplify the square root of 12240 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 12240 and then take the square root of that product. The prime factors that multiply together to make 12240 are 2 x 2 x 2 x 2 x 3 x 3 x 5 x 17. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 3 x 3 = 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Divide 12240 by the number (A) squared. 12 squared is 144 and 12240 divided by 144 is 85. Therefore, B equals 85.

Once again we have A and B and can get our answer to 12240 in its simplest radical form as follows:

√12240 = A√B

√12240 = 12√85

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