Question

simplify.
$8\sqrt{45}$

Explanation:

Step1: Factor the radicand

We know that \(45 = 9\times5\), and \(\sqrt{9\times5}=\sqrt{9}\times\sqrt{5}\) (by the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) for \(a\geq0,b\geq0\)). Since \(\sqrt{9} = 3\), then \(\sqrt{45}=\sqrt{9\times5}=3\sqrt{5}\).

Step2: Multiply with the coefficient

Now we have \(8\sqrt{45}=8\times3\sqrt{5}\). Calculating \(8\times3 = 24\), so \(8\sqrt{45}=24\sqrt{5}\).

Answer:

\(24\sqrt{5}\)