Question

simplify.
$7\sqrt{20}$

Explanation:

Step1: Factor the radicand

We know that \(20 = 4\times5\), and \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (where \(a\geq0,b\geq0\)). So we can rewrite \(\sqrt{20}\) as \(\sqrt{4\times5}\).
\(\sqrt{20}=\sqrt{4\times5}=\sqrt{4}\times\sqrt{5}\)
Since \(\sqrt{4} = 2\), then \(\sqrt{20}=2\sqrt{5}\).

Step2: Multiply by the coefficient

Now we have \(7\sqrt{20}\), substitute \(\sqrt{20}=2\sqrt{5}\) into it:
\(7\sqrt{20}=7\times2\sqrt{5}\)
Calculate \(7\times2 = 14\), so \(7\sqrt{20}=14\sqrt{5}\).

Answer:

\(14\sqrt{5}\)