Question

simplify \\(\sqrt{20}\\)\
\\(\bigcirc\\) a \\(5\sqrt{2}\\)\
\\(\bigcirc\\) b \\(10\sqrt{2}\\)\
\\(\bigcirc\\) c \\(2\sqrt{10}\\)\
\\(\bigcirc\\) d \\(2\sqrt{5}\\)\
\\(\bigcirc\\) e \\(4\sqrt{5}\\)

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 square root property

Use the property \(\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\) (for \(a\geq0, b\geq0\)): \(\sqrt{20}=\sqrt{4\times5}=\sqrt{4}\cdot\sqrt{5}\).

Step3: Simplify the perfect square root

Since \(\sqrt{4} = 2\), we get \(\sqrt{20}=2\sqrt{5}\).

Answer:

D. \(2\sqrt{5}\)