Question

simplify. \\(sqrt{20}\\)

Explanation:

Step1: Factor 20

Factor 20 into a product of a perfect square and another number. We know that \(20 = 4\times5\), where 4 is a perfect square (\(4 = 2^2\)).
\[
\sqrt{20}=\sqrt{4\times5}
\]

Step2: Use square root property

Use the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (for \(a\geq0,b\geq0\)). Here, \(a = 4\) and \(b = 5\), so:
\[
\sqrt{4\times5}=\sqrt{4}\times\sqrt{5}
\]

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

Since \(\sqrt{4}=2\) (because \(2^2 = 4\)), we substitute that in:
\[
\sqrt{4}\times\sqrt{5}=2\sqrt{5}
\]

Answer:

\(2\sqrt{5}\)