Question

question 2 of 6
select the correct answer.
simplify the following radical expression.
$sqrt{48}$
$16sqrt{3}$
$4sqrt{3}$
$4sqrt{2}$
$6sqrt{2}$
submit
reset

Explanation:

Step1: Factor the radicand

We know that \(48 = 16\times3\), so we can rewrite \(\sqrt{48}\) as \(\sqrt{16\times3}\).

Step2: Use the property of square roots

According to the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (where \(a\geq0\) and \(b\geq0\)), we have \(\sqrt{16\times3}=\sqrt{16}\times\sqrt{3}\).

Step3: Simplify \(\sqrt{16}\)

Since \(\sqrt{16} = 4\), then \(\sqrt{16}\times\sqrt{3}=4\sqrt{3}\).

Answer:

\(4\sqrt{3}\) (corresponding to the option "4√3")