Question

9 multiple choice 10 points \\(\sqrt{20}\\) \\(5\sqrt{2}\\) \\(2\sqrt{5}\\) 10 \\(2\sqrt{3}\\)

Explanation:

Step1: Factor the radicand

Factor 20 into a product of a perfect square and another number: \(20 = 4\times5\), where 4 is a perfect square.

Step2: Apply the square - root property

Using the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a\geq0,b\geq0\)), we have \(\sqrt{20}=\sqrt{4\times5}=\sqrt{4}\times\sqrt{5}\).
Since \(\sqrt{4} = 2\), then \(\sqrt{20}=2\sqrt{5}\).

Answer:

\(2\sqrt{5}\) (the option with \(2\sqrt{5}\))