Question

select the correct answer.
simplify the following radical expression.
\\(\sqrt{20}\\)
\\(\circ\\) a. \\(2\sqrt{5}\\)
\\(\circ\\) b. \\(5\sqrt{2}\\)
\\(\circ\\) c. \\(4\sqrt{5}\\)
\\(\circ\\) d. \\(10\sqrt{5}\\)

Explanation:

Step1: Factor the radicand

Factor 20 into a product of a perfect square and another number: \(20 = 4\times5\)
So, \(\sqrt{20}=\sqrt{4\times5}\)

Step2: Use the property of square roots

Use the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (where \(a\geq0,b\geq0\)): \(\sqrt{4\times5}=\sqrt{4}\times\sqrt{5}\)

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

Since \(\sqrt{4} = 2\), we have \(\sqrt{4}\times\sqrt{5}=2\sqrt{5}\)

Answer:

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