Question

$-sqrt{27} - 3sqrt{45} - sqrt{20}$

Explanation:

Step1: Simplify each square root

Simplify $\sqrt{27}$, $\sqrt{45}$, and $\sqrt{20}$ by factoring out perfect squares.
$\sqrt{27}=\sqrt{9\times3}=3\sqrt{3}$
$3\sqrt{45}=3\sqrt{9\times5}=3\times3\sqrt{5}=9\sqrt{5}$
$\sqrt{20}=\sqrt{4\times5}=2\sqrt{5}$

Step2: Substitute the simplified roots back

Substitute these back into the original expression:
$-\sqrt{27}-3\sqrt{45}-\sqrt{20}=-3\sqrt{3}-9\sqrt{5}-2\sqrt{5}$

Step3: Combine like terms

Combine the terms with $\sqrt{5}$:
$-3\sqrt{3}+(-9\sqrt{5}-2\sqrt{5})=-3\sqrt{3}-11\sqrt{5}$

Answer:

$-3\sqrt{3}-11\sqrt{5}$