1) Don't use square roots as a method. They may be the result of other, appropriate methods.
2) You simply must learn to recognize certain patterns that will simplfy your life. The "Difference of Squares" is one such pattern. They are very easy to factor.
3) This one isn't quite a difference of squares, but it can be made to be such.
3x^2 - 27 = 0
Divide by 3
x^2 - 9 = 0
That is a Difference of Squares and is easily factored.
(x+3)(x-3) = 0
Therefore, x = 3 or x = -3
I didn't see a square root in there. Why do you believe you needed one?