Simplify Square Root of 12096

Here we will show you two methods that you can use to simplify the square root of 12096. In other words, we will show you how to find the square root of 12096 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.

√12096 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 12096 to simplify the square root of 12096. 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 12096. The factors of 12096 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 27, 28, 32, 36, 42, 48, 54, 56, 63, 64, 72, 84, 96, 108, 112, 126, 144, 168, 189, 192, 216, 224, 252, 288, 336, 378, 432, 448, 504, 576, 672, 756, 864, 1008, 1344, 1512, 1728, 2016, 3024, 4032, 6048, and 12096. Furthermore, the greatest perfect square on this list is 576 and the square root of 576 is 24. Therefore, A equals 24.

B = Calculate 12096 divided by the greatest perfect square from the list of all factors of 12096. We determined above that the greatest perfect square from the list of all factors of 12096 is 576. Furthermore, 12096 divided by 576 is 21, therefore B equals 21.

Now we have A and B and can get our answer to 12096 in its simplest radical form as follows:

√12096 = A√B

√12096 = 24√21

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 12096 to simplify the square root of 12096 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 12096 and then take the square root of that product. The prime factors that multiply together to make 12096 are 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 7. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 = 576 and the square root of 576 is 24. Therefore, A equals 24.

B = Divide 12096 by the number (A) squared. 24 squared is 576 and 12096 divided by 576 is 21. Therefore, B equals 21.

Once again we have A and B and can get our answer to 12096 in its simplest radical form as follows:

√12096 = A√B

√12096 = 24√21

Simplify Square Root
Please enter another square root in the box below for us to simplify.

Simplify Square Root of 12097
Here is the next square root on our list that we have simplifed for you.