which of the following is a like radical to $3xsqrt{5}$?\n$x(sqrt3{5})$\n$sqrt{5y}$\n$3(sqrt3{5x})$\n$ysqrt{5…

Answer:

D. $y\sqrt{5}$

Explanation:

Step1: Recall like - radical definition

Like radicals have the same index and the same radicand. The given radical $3x\sqrt{5}$ has an index of 2 (square - root) and radicand of 5.

Step2: Analyze each option

• Option A: $x\sqrt[3]{5}$ has an index of 3, different from the index of 2 in $3x\sqrt{5}$.
• Option B: $\sqrt{5y}$ has a radicand of 5y, different from the radicand of 5 in $3x\sqrt{5}$.
• Option C: $3\sqrt[3]{5x}$ has an index of 3, different from the index of 2 in $3x\sqrt{5}$.
• Option D: $y\sqrt{5}$ has an index of 2 and radicand of 5, same as $3x\sqrt{5}$.