## Introductory Algebra for College Students (7th Edition)

$$3x\sqrt 7$$
We can use the product rule for square roots to rewrite the radicand as a product of the greatest perfect square factor and another factor. We can see that the radicand $63x^3$ can be broken down into two factors: the perfect square $9x^2$ and $7$: $$(\sqrt 9x^2)(\sqrt 7)$$ Because $9x^2$ is a perfect square, we go ahead and simplify the expression by taking the square root of $9x^2$, which is $3x$: $$3x\sqrt 7$$