Question

find the product in simplest radical form.
$2\sqrt3{-14} \cdot 4\sqrt3{28}$

Explanation:

Step1: Multiply coefficients and radicals

$2 \cdot 4 \cdot \sqrt[3]{-14 \cdot 28}$

Step2: Calculate products inside/outside

$8 \cdot \sqrt[3]{-392}$

Step3: Factor radicand for cube roots

$-392 = -8 \cdot 49$, so $8 \cdot \sqrt[3]{-8 \cdot 49}$

Step4: Simplify the cube root

$8 \cdot (-2) \cdot \sqrt[3]{49}$

Step5: Multiply remaining coefficients

$8 \times (-2) = -16$

Answer:

$-16\sqrt[3]{49}$