Question

simplify the expression. assume all variables represent positive real numbers. (sqrt3{4x}cdotsqrt3{9y}) select the correct choice below and fill in any answer boxes in your choice. a. (sqrt3{4x}cdotsqrt3{9y}=) (simplify your answer. type an exact answer, using radicals as needed.) b. the expression cannot be simplified.

Explanation:

Step1: Use product - rule of radicals

The product - rule of radicals states that $\sqrt[n]{a}\cdot\sqrt[n]{b}=\sqrt[n]{ab}$ for $n\geq2$ and $a,b\geq0$. Here $n = 3$, $a = 4x$ and $b=9y$. So, $\sqrt[3]{4x}\cdot\sqrt[3]{9y}=\sqrt[3]{4x\cdot9y}$.

Step2: Multiply the coefficients inside the radical

Multiply $4$ and $9$: $4\times9 = 36$. Then $\sqrt[3]{4x\cdot9y}=\sqrt[3]{36xy}$.

Answer:

A. $\sqrt[3]{4x}\cdot\sqrt[3]{9y}=\sqrt[3]{36xy}$