Question

4 multiple choice 10 points \\(\sqrt{18}\\) \\(2\sqrt{3}\\) \\(9\\) \\(3\sqrt{2}\\) \\(2\sqrt{9}\\)

Explanation:

Step1: Factor 18 into prime factors

We know that \(18 = 9\times2\), and \(9\) is a perfect square. So we can rewrite \(\sqrt{18}\) as \(\sqrt{9\times2}\).

Step2: Use the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (where \(a\geq0,b\geq0\))

Applying this property, \(\sqrt{9\times2}=\sqrt{9}\times\sqrt{2}\).

Step3: Simplify \(\sqrt{9}\)

Since \(\sqrt{9} = 3\), then \(\sqrt{9}\times\sqrt{2}=3\sqrt{2}\).

Answer:

\(3\sqrt{2}\) (the option with "3√2")