Question

simplify the expression.
\sqrt{3} \cdot \sqrt{32}

Explanation:

Step1: Simplify $\sqrt{32}$

We know that $32 = 16\times2$, and $\sqrt{16\times2}=\sqrt{16}\times\sqrt{2}$ (by the property $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ for $a\geq0,b\geq0$). Since $\sqrt{16} = 4$, then $\sqrt{32}=4\sqrt{2}$.

Step2: Multiply $\sqrt{3}$ and $4\sqrt{2}$

Using the property $a\sqrt{b}\times c\sqrt{d}=ac\sqrt{bd}$ (for $b\geq0,d\geq0$), we have $\sqrt{3}\times4\sqrt{2}=4\times\sqrt{3\times2}=4\sqrt{6}$.

Answer:

$4\sqrt{6}$