three radical expressions have different radicands and, when simplified, are like radicals to $sqrt{3xy}$…
three radical expressions have different radicands and, when simplified, are like radicals to $sqrt{3xy}$. describe key characteristics of these radical expressions.
Answer
Brief Explanations:
Like - radicals have the same index and the same radicand after simplification. Since the given radical is $\sqrt{3xy}$ (index 2), the three radical expressions must have an index of 2. Before simplification, their radicands are different, but they can be factored in such a way that after simplification, the non - square factors are 3, x, and y. For example, they could be $\sqrt{12xy}$, $\sqrt{27xy}$, $\sqrt{75xy}$ which simplify to $2\sqrt{3xy}$, $3\sqrt{3xy}$, $5\sqrt{3xy}$ respectively.
Answer:
The key characteristics are: 1. The index of each radical expression is 2. 2. After simplification, the radicand is 3xy. 3. Before simplification, the radicands are different but can be factored to have 3xy as a non - square factor after simplification.