Question

1. simplify: $3\sqrt{72}$

Explanation:

Step1: Factor 72 into perfect square and other

We know that \(72 = 36\times2\), where \(36\) is a perfect square. So, \(\sqrt{72}=\sqrt{36\times2}\).

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 \(\sqrt{36\times2}=\sqrt{36}\times\sqrt{2}\). Since \(\sqrt{36} = 6\), then \(\sqrt{36}\times\sqrt{2}=6\sqrt{2}\).

Step3: Multiply by the coefficient 3

We have \(3\sqrt{72}=3\times6\sqrt{2}\). And \(3\times6 = 18\), so \(3\times6\sqrt{2}=18\sqrt{2}\).

Answer:

\(18\sqrt{2}\)