Question

simplify.
-5√45 -√20

Explanation:

Step1: Simplify each square root

First, simplify \(\sqrt{45}\). We can factor 45 as \(9\times5\), and since \(\sqrt{9\times5}=\sqrt{9}\times\sqrt{5}=3\sqrt{5}\). Then simplify \(\sqrt{20}\). Factor 20 as \(4\times5\), so \(\sqrt{4\times5}=\sqrt{4}\times\sqrt{5}=2\sqrt{5}\).

Step2: Substitute back into the expression

Now substitute these simplified forms back into the original expression: \(-5\sqrt{45}-\sqrt{20}=-5\times3\sqrt{5}-2\sqrt{5}\).

Step3: Perform the multiplication and combine like terms

Calculate \(-5\times3\sqrt{5}=-15\sqrt{5}\). Now the expression becomes \(-15\sqrt{5}-2\sqrt{5}\). Since both terms have \(\sqrt{5}\), we can combine them: \((-15 - 2)\sqrt{5}=-17\sqrt{5}\).

Answer:

\(-17\sqrt{5}\)