Multiply and then, if possible, simplify by factoring.
-$\sqrt{x^{8} y^{2}} \sqrt{x y^{7}}$
A) $x^{4} y^{4} \sqrt{x y}$
B) $x^{8} y^{8} \sqrt{x y}$
C) $\sqrt{x^{9} y^{9}}$
D) $x^{4} \sqrt{x y^{9}}$

Question

Quizplus · Accepted Answer

Multiplying the two square roots together gives $\sqrt{x^{8} y^{2} \cdot x y^{7}} = \sqrt{x^{9} y^{9}}$. Simplifying this by factoring out perfect squares results in $x^{4} y^{4} \sqrt{x y}$, since $x^{9} = x^{8} \cdot x$ and $y^{9} = y^{8} \cdot y$, and $\sqrt{x^{8}} = x^{4}$, $\sqrt{y^{8}} = y^{4}$.

Multiply and Then, If Possible, Simplify by Factoring x8y2xy7\sqrt{x^{8} y^{2}} \sqrt{x y^{7}}x8y2​xy7​

Multiply and Then, If Possible, Simplify by Factoring $\sqrt{x^{8} y^{2}} \sqrt{x y^{7}}$