Intermediate Algebra for College Students (7th Edition)

Since, $\sqrt{ab}=\sqrt a \sqrt b$ Thus, $\sqrt[n]{ab}=\sqrt[n] a \sqrt[n] b$ Here, $n$ refers as index. If two radicals will have have same index then their product will also have same index. such as: Since, $\sqrt[3] 4 \cdot \sqrt[3] 4=\sqrt[3]{4 \cdot 4}=\sqrt [3]{16} \ne 4$ Hence, the statement false.