Question

simplify the following square root.
$2\sqrt{18}$

Explanation:

Step1: Factor the radicand

We factor 18 into a product of a perfect square and another number. Since \(18 = 9\times2\) and 9 is a perfect square (\(9 = 3^2\)), we can rewrite \(\sqrt{18}\) as \(\sqrt{9\times2}\).
Using 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 \(\sqrt{9} = 3\), this simplifies to \(3\sqrt{2}\).

Step2: Multiply by the coefficient

Now we have the original expression \(2\sqrt{18}\), and we just found that \(\sqrt{18}=3\sqrt{2}\). So we multiply 2 by 3\(\sqrt{2}\).
\(2\times3\sqrt{2}=6\sqrt{2}\).

Answer:

\(6\sqrt{2}\)