13
QuizMultiple Choice

N/A — Exam

Question 13 • Algebra II

What is the following sum? 2 times open paren cube root of 16 x cubed y close paren plus 4 times open paren cube root of 54 x to the 6th power y to the 5th power close paren

Answer
A
16 x cubed y open paren cube root of 2 y squared close paren
B
48 x cubed y open paren cube root of 2 y close paren
C
8 x open paren cube root of x y close paren plus 12 x cubed y squared open paren cube root of 6 y close paren
D
4 x open paren cube root of 2 y close paren plus 12 x squared y open paren cube root of 2 y squared close paren

Explanation

Simplify each cube root by taking out perfect cubes: ∛(16x³y) = 2x∛(2y), so the first term becomes 4x∛(2y). Also, ∛(54x⁶y⁵) = 3x²y∛(2y²), so the second term becomes 12x²y∛(2y²). Together these match choice D.

AI-written and checked against the verified answer.

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