## Intermediate Algebra (12th Edition)

The product rule for radicals tells us that $\sqrt[n] a\times\sqrt[n] b=\sqrt[n] ab$ (when $\sqrt[n] a$ and $\sqrt[n] b$ are real numbers and $n$ is a natural number). That is, the product of two nth roots is the nth root of the product. Therefore, $\sqrt[3] 7 \times\sqrt[4] 3$ cannot be simplified using the product rule because the indexes (3 and 4) are different.