Question

simplify.
$4\sqrt{18}$

Explanation:

Step1: Factor the radicand

We know that \(18 = 9\times2\), and \(9\) is a perfect square. So we can rewrite \(\sqrt{18}\) as \(\sqrt{9\times2}\).
According to the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (where \(a\geq0\) and \(b\geq0\)), we have \(\sqrt{9\times2}=\sqrt{9}\times\sqrt{2}\).
Since \(\sqrt{9} = 3\), then \(\sqrt{18}=3\sqrt{2}\).

Step2: Multiply by the coefficient

Now we have \(4\sqrt{18}\), substitute \(\sqrt{18}=3\sqrt{2}\) into it, we get \(4\times3\sqrt{2}\).
Calculate \(4\times3 = 12\), so \(4\sqrt{18}=12\sqrt{2}\).

Answer:

\(12\sqrt{2}\)