Question

simplify $3\sqrt{18}$

Explanation:

Step1: Factor 18 into prime factors

We know that \(18 = 9\times2\), and \(9 = 3^2\). So we can rewrite \(\sqrt{18}\) as \(\sqrt{9\times2}\).

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 \(\sqrt{9\times2}=\sqrt{9}\times\sqrt{2}\). Since \(\sqrt{9} = 3\), then \(\sqrt{18}=3\sqrt{2}\).

Step3: Substitute back into the original expression

The original expression is \(3\sqrt{18}\). Substitute \(\sqrt{18} = 3\sqrt{2}\) into it, we get \(3\times(3\sqrt{2})\).

Step4: Simplify the multiplication

\(3\times(3\sqrt{2})=(3\times3)\sqrt{2}=9\sqrt{2}\).

Answer:

\(9\sqrt{2}\)