## Algebra 2 Common Core

$2xy\sqrt{2}$
The variables are assumed to be non-zero since they are also in the denominator. RECALL: $\dfrac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$ where $a$ and $b$ are non-negative and $b\ne0.$ Use the rule above to have $\require{cancel} \sqrt{\dfrac{56x^5y^5}{7xy}} \\=\sqrt{\dfrac{\cancel{56}8\cancel{x^5}x^4\cancel{y^5}y^4}{\cancel{7xy}}} \\=\sqrt{8x^4y^4} \\=\sqrt{4x^4y^4(2)} \\=\sqrt{(2x^2y^2)^2(2)} \\=2xy\sqrt{2}.$