Simplify Square Root of 11988

Here we will show you two methods that you can use to simplify the square root of 11988. In other words, we will show you how to find the square root of 11988 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.

√11988 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 11988 to simplify the square root of 11988. 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 11988. The factors of 11988 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 37, 54, 74, 81, 108, 111, 148, 162, 222, 324, 333, 444, 666, 999, 1332, 1998, 2997, 3996, 5994, and 11988. Furthermore, the greatest perfect square on this list is 324 and the square root of 324 is 18. Therefore, A equals 18.

B = Calculate 11988 divided by the greatest perfect square from the list of all factors of 11988. We determined above that the greatest perfect square from the list of all factors of 11988 is 324. Furthermore, 11988 divided by 324 is 37, therefore B equals 37.

Now we have A and B and can get our answer to 11988 in its simplest radical form as follows:

√11988 = A√B

√11988 = 18√37

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 11988 to simplify the square root of 11988 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 11988 and then take the square root of that product. The prime factors that multiply together to make 11988 are 2 x 2 x 3 x 3 x 3 x 3 x 37. When we strip out the pairs only, we get 2 x 2 x 3 x 3 x 3 x 3 = 324 and the square root of 324 is 18. Therefore, A equals 18.

B = Divide 11988 by the number (A) squared. 18 squared is 324 and 11988 divided by 324 is 37. Therefore, B equals 37.

Once again we have A and B and can get our answer to 11988 in its simplest radical form as follows:

√11988 = A√B

√11988 = 18√37

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Simplify Square Root of 11989
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