SAT Question e117d3b8: Equivalent Expressions answer and explanation with Desmos solution

Choice C is correct. Using the property that $\sqrt{x}\sqrt{y}=\sqrt{xy}$ for positive numbers $x$ and $y$, with $x=(a+c{)}^3$ and $y=a+c$, it follows that $\sqrt{(a+c{)}^3}\sqrt{a+c}=\sqrt{(a+c{)}^4}$. By rewriting $(a+c{)}^4$ as $((a+c{)}^2{)}^2$, it is possible to simplify the square root expression as follows: $\sqrt{((a+c{)}^2{)}^2}=(a+c{)}^2=a^2+2ac+c^2$.