Question

use the properties of radicals to simplify the expression.
$\frac{sqrt3{6} cdot sqrt3{72}}{sqrt3{2}} = \square$

Explanation:

Step1: Combine radicals (product/quotient rule)

$\frac{\sqrt[3]{6 \cdot 72}}{\sqrt[3]{2}} = \sqrt[3]{\frac{6 \cdot 72}{2}}$

Step2: Simplify inside the radical

First calculate $\frac{72}{2}=36$, then $6 \cdot 36 = 216$. So we get $\sqrt[3]{216}$

Step3: Evaluate the cube root

$\sqrt[3]{216} = 6$ since $6^3 = 216$

Answer:

$6$