Question

#1: radicals
for all positive values of $x$, which of the following expressions is equivalent to $2\sqrt3{2x} \cdot \sqrt3{x}$ ?
f. $\sqrt3{12x}$
g. $\sqrt3{24x}$
h. $\sqrt3{4x^2}$
j. $\sqrt3{8x^2}$
k. $\sqrt3{16x^2}$

Explanation:

Step1: Multiply the cube roots

$2\sqrt[3]{2x} \cdot \sqrt[3]{x} = 2\sqrt[3]{2x \cdot x}$

Step2: Simplify the radicand

$2\sqrt[3]{2x^2}$

Step3: Move coefficient inside the cube root

$2\sqrt[3]{2x^2} = \sqrt[3]{2^3 \cdot 2x^2} = \sqrt[3]{8 \cdot 2x^2}$

Step4: Calculate product inside the root

$\sqrt[3]{16x^2}$

Answer:

K. $\sqrt[3]{16x^2}$