Question

simplify \\(\sqrt{20}\\). the simplified expression is \\(\square\\).

Explanation:

Step1: Factor 20 into perfect square and other factor

We know that \(20 = 4\times5\), where \(4\) is a perfect square (\(4 = 2^2\)). So we can rewrite \(\sqrt{20}\) as \(\sqrt{4\times5}\).

Step2: Use the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (for \(a\geq0,b\geq0\))

Applying the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) to \(\sqrt{4\times5}\), we get \(\sqrt{4}\times\sqrt{5}\).

Step3: Simplify \(\sqrt{4}\)

Since \(\sqrt{4} = 2\) (because \(2^2=4\)), the expression becomes \(2\times\sqrt{5}\) or \(2\sqrt{5}\).

Answer:

\(2\sqrt{5}\)