Choose the one alternative that best completes the statement or answers the question.
Multiply. Assume all variables represent nonnegative real numbers.
-$\sqrt [ 3 ] { 175 } \cdot \sqrt [ 3 ] { 25 }$
A) $5 \sqrt [ 3 ] { 35 }$
B) $10 \sqrt [ 3 ] { 35 }$
C) $10 \sqrt [ 3 ] { 15 }$
D) $5 \sqrt [ 3 ] { 25 }$

Question

Quizplus · Accepted Answer

When multiplying cube roots, you can combine them under a single cube root and then simplify: $\sqrt[3]{175} \cdot \sqrt[3]{25} = \sqrt[3]{175 \cdot 25} = \sqrt[3]{4375}$. Factoring 4375, we find it is $5^3 \cdot 7$, so $\sqrt[3]{5^3 \cdot 7} = 5\sqrt[3]{7}$, which simplifies to $5\sqrt[3]{35}$.

Choose the One Alternative That Best Completes the Statement or Answers