To solve this expression, we need to simplify the terms inside the square roots first.

√(27-√300+18) = √(45-√300)

Next, let's simplify the term inside the square root.

√(45-√300) = √(45-√(100*3))
= √(45-√100√3)
= √(45-10√3)

Now, we can plug this back into our original expression:

(√(27-√300+18) x √3) + √24 = (√(45-10√3) x √3) + √24
= (√135 - 30) + √24
= (√(3^3 x 5) - 30) + √(4 x 6)
= (3√5 - 30) + 2√6

Therefore, the final simplified expression is (3√5 - 30) + 2√6