Question

simplify.
$9\sqrt{18}$

Explanation:

Step1: Factor 18 into perfect square and other

We know that \(18 = 9\times2\), where 9 is a perfect square. So, \(\sqrt{18}=\sqrt{9\times2}\).

Step2: Use 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 \(\sqrt{9}\times\sqrt{2}=3\sqrt{2}\).

Step3: Multiply with the coefficient 9

We have \(9\sqrt{18}=9\times\sqrt{18}\), and we just found that \(\sqrt{18} = 3\sqrt{2}\), so \(9\times3\sqrt{2}=27\sqrt{2}\).

Answer:

\(27\sqrt{2}\)