-square root of 27 - 3square root of 45-square root of 20+2square root of 45
-√27 - 3√45 - √20 + 2√45
= -3√3 - 9√5 - 2√5 + 6√5
= -5√5 - 3√3
-3√18+3√8-√24
To simplify the given expression:
-√27 - 3√45 - √20 + 2√45
We can simplify each radical term individually and then combine like terms.
Let's start with simplifying the square roots of the numbers inside the radicals:
√27 = √(9 × 3) = √9 × √3 = 3√3
√45 = √(9 × 5) = √9 × √5 = 3√5
√20 = √(4 × 5) = √4 × √5 = 2√5
Now let's substitute these values back into the original expression:
3√3 - 3(3√5) - 2√5 + 2(3√5)
Next, we simplify the expression further by combining like terms.
Starting with the terms that have √5:
-3(3√5) + 2(3√5) = -9√5 + 6√5 = -3√5
Now, let's combine the remaining terms:
3√3 - 3√5 - 2√5
Combine -3√5 and -2√5:
-3√5 - 2√5 = -5√5
Finally, our simplified expression becomes:
3√3 - 5√5
So, the simplified expression is 3√3 - 5√5.