Question

simplify $3\sqrt{5} - 2\sqrt{20}$.

Explanation:

Step1: Simplify \(\sqrt{20}\)

We know that \(20 = 4\times5\), so \(\sqrt{20}=\sqrt{4\times5}\). Using the property \(\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\) (\(a\geq0,b\geq0\)), we get \(\sqrt{4\times5}=\sqrt{4}\cdot\sqrt{5}=2\sqrt{5}\).

Step2: Substitute back into the original expression

The original expression is \(3\sqrt{5}-2\sqrt{20}\). Substituting \(\sqrt{20} = 2\sqrt{5}\), we have \(3\sqrt{5}-2\times(2\sqrt{5})\).

Step3: Simplify the expression

First, calculate \(2\times(2\sqrt{5}) = 4\sqrt{5}\). Then the expression becomes \(3\sqrt{5}-4\sqrt{5}\). Combining like terms (since both terms have \(\sqrt{5}\)), we get \((3 - 4)\sqrt{5}=-\sqrt{5}\).

Answer:

\(-\sqrt{5}\)