Question

find the product in simplest radical form.
$2\sqrt3{-14} \cdot 4\sqrt3{28}$
root symbol ($\sqrt{\square}$), type
oot\

Explanation:

Step1: Multiply the coefficients

$2 \times 4 = 8$

Step2: Multiply the radicands

$\sqrt[3]{-14} \times \sqrt[3]{28} = \sqrt[3]{-14 \times 28}$

Step3: Simplify the product inside radical

$-14 \times 28 = -392 = -8 \times 49$

Step4: Split the cube root

$\sqrt[3]{-8 \times 49} = \sqrt[3]{-8} \times \sqrt[3]{49} = -2\sqrt[3]{49}$

Step5: Multiply with coefficient

$8 \times (-2\sqrt[3]{49}) = -16\sqrt[3]{49}$

Answer:

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