Question

$\sqrt{8}\cdot\sqrt{3}=$
$2\sqrt{6}$
$12\sqrt{2}$
$\sqrt{11}$
$4\sqrt{6}$

Explanation:

Step1: Use property of square roots

Recall that \(\sqrt{a} \cdot \sqrt{b}=\sqrt{ab}\) for \(a\geq0\) and \(b\geq0\). So, \(\sqrt{8}\cdot\sqrt{3}=\sqrt{8\times3}\)

Step2: Simplify the product inside the square root

Calculate \(8\times3 = 24\), so we have \(\sqrt{24}\)

Step3: Simplify \(\sqrt{24}\)

Factor \(24\) as \(4\times6\), then \(\sqrt{24}=\sqrt{4\times6}\). Using the property \(\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\) again, we get \(\sqrt{4}\cdot\sqrt{6}\)

Step4: Evaluate \(\sqrt{4}\)

Since \(\sqrt{4} = 2\), we have \(2\sqrt{6}\)

Answer:

\(2\sqrt{6}\) (corresponding to the option with text \(2\sqrt{6}\))