Question

algebra: concepts and connections - plc rewriting expressions with radicals combine and simplify these radicals. \\(\sqrt{3} \cdot \sqrt{16}\\) options: \\(3\sqrt{16}\\), \\(16\sqrt{3}\\), \\(3\sqrt{4}\\), \\(4\sqrt{3}\\)

Explanation:

Step1: Apply radical product rule

$\sqrt{3} \cdot \sqrt{16} = \sqrt{3 \cdot 16}$

Step2: Simplify product inside radical

$\sqrt{48} = \sqrt{16 \cdot 3}$

Step3: Split radical using product rule

$\sqrt{16 \cdot 3} = \sqrt{16} \cdot \sqrt{3}$

Step4: Evaluate $\sqrt{16}$

$4 \cdot \sqrt{3} = 4\sqrt{3}$

Answer:

$4\sqrt{3}$