Question

simplify.
$5\sqrt{12}$

Explanation:

Step1: Factor the radicand

We know that \(12 = 4\times3\), and \(\sqrt{4\times3}=\sqrt{4}\times\sqrt{3}\) (by the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) for \(a\geq0,b\geq0\)). Since \(\sqrt{4} = 2\), we can rewrite \(\sqrt{12}\) as \(2\sqrt{3}\).

Step2: Multiply by the coefficient

Now we have \(5\sqrt{12}=5\times(2\sqrt{3})\). Multiplying the coefficients \(5\) and \(2\) gives \(10\), so \(5\times(2\sqrt{3}) = 10\sqrt{3}\).

Answer:

\(10\sqrt{3}\)