Question

simplify.
$7\sqrt{20}$

Explanation:

Step1: Factor the radicand

We know that \(20 = 4\times5\), and \(4\) is a perfect square. So we can rewrite \(\sqrt{20}\) as \(\sqrt{4\times5}\).
\(7\sqrt{20}=7\sqrt{4\times5}\)

Step2: Use the property of square roots

The property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (where \(a\geq0\), \(b\geq0\)) allows us to split the square root. So \(\sqrt{4\times5}=\sqrt{4}\times\sqrt{5}\). Since \(\sqrt{4} = 2\), we have:
\(7\sqrt{4\times5}=7\times\sqrt{4}\times\sqrt{5}=7\times2\times\sqrt{5}\)

Step3: Multiply the coefficients

Multiply \(7\) and \(2\) to get \(14\). So the simplified form is:
\(14\sqrt{5}\)

Answer:

\(14\sqrt{5}\)