Question

simplify.
\sqrt{18}

Explanation:

Step1: Factor 18 into prime factors

We know that \(18 = 9\times2\), and \(9 = 3^2\), so \(18=3^2\times2\).

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

\(\sqrt{18}=\sqrt{3^2\times2}=\sqrt{3^2}\times\sqrt{2}\)

Step3: Simplify \(\sqrt{3^2}\)

Since \(\sqrt{a^2}=a\) for \(a\geq0\), then \(\sqrt{3^2} = 3\). So \(\sqrt{3^2}\times\sqrt{2}=3\sqrt{2}\)

Answer:

\(3\sqrt{2}\)