Perform the indicated operation. Simplify, if possible. Assume all variables are positive. $\sqrt { 12 x ^ { 9 } y ^ { 9 } } \cdot \sqrt { 8 x ^ { 2 } y ^ { 4 } }$
A) $4 x ^ { 4 } y ^ { 13 } \sqrt { 6 }$
B) $4 x ^ { 5 } y ^ { 6 } \sqrt { 6 x y }$
C) $4 x ^ { 7 } y ^ { 5 } \sqrt { 6 x }$
D) none of these

Question

Quizplus · Accepted Answer

First, simplify inside the square roots: $\sqrt{12x^9y^9} = \sqrt{4\cdot3x^9y^9} = 2x^{4.5}y^{4.5}$ and $\sqrt{8x^2y^4} = \sqrt{4\cdot2x^2y^4} = 2xy^2$. Multiplying these gives $4x^{5.5}y^{6.5}$, which simplifies to $4x^5y^6\sqrt{xy}$, matching option B.

Perform the Indicated Operation 12x9y9⋅8x2y4\sqrt { 12 x ^ { 9 } y ^ { 9 } } \cdot \sqrt { 8 x ^ { 2 } y ^ { 4 } }12x9y9​⋅8x2y4​

Perform the Indicated Operation $\sqrt { 12 x ^ { 9 } y ^ { 9 } } \cdot \sqrt { 8 x ^ { 2 } y ^ { 4 } }$