Simplify Square Root of 27972

Here we will show you two methods that you can use to simplify the square root of 27972. In other words, we will show you how to find the square root of 27972 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.

√27972 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 27972 to simplify the square root of 27972. 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 27972. The factors of 27972 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 37, 42, 54, 63, 74, 84, 108, 111, 126, 148, 189, 222, 252, 259, 333, 378, 444, 518, 666, 756, 777, 999, 1036, 1332, 1554, 1998, 2331, 3108, 3996, 4662, 6993, 9324, 13986, and 27972. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 27972 divided by the greatest perfect square from the list of all factors of 27972. We determined above that the greatest perfect square from the list of all factors of 27972 is 36. Furthermore, 27972 divided by 36 is 777, therefore B equals 777.

Now we have A and B and can get our answer to 27972 in its simplest radical form as follows:

√27972 = A√B

√27972 = 6√777

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 27972 to simplify the square root of 27972 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 27972 and then take the square root of that product. The prime factors that multiply together to make 27972 are 2 x 2 x 3 x 3 x 3 x 7 x 37. When we strip out the pairs only, we get 2 x 2 x 3 x 3 = 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Divide 27972 by the number (A) squared. 6 squared is 36 and 27972 divided by 36 is 777. Therefore, B equals 777.

Once again we have A and B and can get our answer to 27972 in its simplest radical form as follows:

√27972 = A√B

√27972 = 6√777

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