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
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