Multiply the radical expressions and simplify your answer.
$- 2 \sqrt { 6 x ^ { 8 } y ^ { 3 } } \cdot 4 \sqrt { 10 x y ^ { 8 } }$

A) $- 32 x ^ { 4 } y ^ { 5 } \sqrt { 15 x y }$
B) $- 32 \sqrt { x ^ { 7 } y ^ { 9 } }$
C) $- 16 \sqrt { 15 x ^ { 9 } y ^ { 11 } }$
D) $- 16 x ^ { 4 } y ^ { 5 } \sqrt { 15 x y }$

Question

Multiply the radical expressions and simplify your answer. 
$- 2 \sqrt { 6 x ^ { 8 } y ^ { 3 } } \cdot 4 \sqrt { 10 x y ^ { 8 } }$

A) $- 32 x ^ { 4 } y ^ { 5 } \sqrt { 15 x y }$
B) $- 32 \sqrt { x ^ { 7 } y ^ { 9 } }$
C) $- 16 \sqrt { 15 x ^ { 9 } y ^ { 11 } }$
D) $- 16 x ^ { 4 } y ^ { 5 } \sqrt { 15 x y }$

Quizplus · Accepted Answer

To multiply the given radical expressions, first multiply the coefficients and then multiply the radicands (the expressions inside the square roots) together. The multiplication gives: $-2 \cdot 4 = -8$ and $\sqrt{6x^8y^3} \cdot \sqrt{10xy^8} = \sqrt{60x^9y^{11}}$. Simplifying inside the square root, we can take out perfect squares, resulting in $-8 \cdot x^4y^5\sqrt{15xy} = -16x^4y^5\sqrt{15xy}$, matching option D.

Multiply the Radical Expressions and Simplify Your Answer −26x8y3⋅410xy8- 2 \sqrt { 6 x ^ { 8 } y ^ { 3 } } \cdot 4 \sqrt { 10 x y ^ { 8 } }−26x8y3​⋅410xy8​

Multiply the Radical Expressions and Simplify Your Answer $- 2 \sqrt { 6 x ^ { 8 } y ^ { 3 } } \cdot 4 \sqrt { 10 x y ^ { 8 } }$