Question

10 multiple choice 10 points \\(\sqrt{27}\\) \\(6\sqrt{2}\\) \\(4\sqrt{3}\\) \\(5\sqrt{5}\\) \\(3\sqrt{3}\\)

Explanation:

Step1: Factor the radicand

We know that \(27 = 9\times3\), so \(\sqrt{27}=\sqrt{9\times3}\).

Step2: Use the square - root property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a\geq0,b\geq0\))

According to the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\), we have \(\sqrt{9\times3}=\sqrt{9}\times\sqrt{3}\).
Since \(\sqrt{9} = 3\), then \(\sqrt{9}\times\sqrt{3}=3\sqrt{3}\).

Answer:

\(3\sqrt{3}\) (the last option: \(3\sqrt{3}\))