Multiply the radical expressions and simplify your answer.
-$- 3 \sqrt { 6 x ^ { 6 } y ^ { 3 } } \cdot 2 \sqrt { 10 x y ^ { 6 } }$
A) $- 24 x ^ { 3 } y ^ { 4 } \sqrt { 15 x y }$
B) $- 12 x ^ { 3 } y ^ { 4 } \sqrt { 15 x y }$
C) $- 24 x y \sqrt { x ^ { 5 } y ^ { 7 } }$
D) $- 12 \sqrt { 15 x ^ { 7 } y ^ { 9 } }$

Question

Quizplus · Accepted Answer

When multiplying radical expressions, you multiply the coefficients together and the radicands together separately. Here, $-3 \cdot 2 = -6$, and $\sqrt{6x^6y^3} \cdot \sqrt{10xy^6} = \sqrt{60x^7y^9}$. Simplifying inside the radical, $60 = 15 \cdot 4$, and $x^7y^9 = x^3y^4 \cdot x^4y^5$, so the expression becomes $-6 \cdot 2x^3y^4\sqrt{15xy}$, which simplifies to $-12x^3y^4\sqrt{15xy}$.

Multiply the Radical Expressions and Simplify Your Answer −36x6y3⋅210xy6- 3 \sqrt { 6 x ^ { 6 } y ^ { 3 } } \cdot 2 \sqrt { 10 x y ^ { 6 } }−36x6y3​⋅210xy6​

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