Question

which expression is equivalent to $8x^{2}\sqrt3{375x} + 2\sqrt3{3x^{7}}$, if $x \
eq 0$?\
\
a. $42x^{3}$\
\
b. $10x^{4}\sqrt3{125x}$\
\
c. $10x^{2}\sqrt3{125x^{3}}$\
\
d. $42x^{2}\sqrt3{3x}$

Explanation:

Step1: Simplify $\sqrt[3]{375x}$

$\sqrt[3]{375x} = \sqrt[3]{125 \times 3x} = 5\sqrt[3]{3x}$

Step2: Simplify first term

$8x^2 \times 5\sqrt[3]{3x} = 40x^2\sqrt[3]{3x}$

Step3: Simplify $\sqrt[3]{3x^7}$

$\sqrt[3]{3x^7} = \sqrt[3]{3x^6 \times x} = x^2\sqrt[3]{3x}$

Step4: Simplify second term

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

Step5: Combine the two terms

$40x^2\sqrt[3]{3x} + 2x^2\sqrt[3]{3x} = 42x^2\sqrt[3]{3x}$

Answer:

D. $42x^{2}\sqrt [3]{3x}$