Introductory Algebra for College Students (7th Edition)

$$5x\sqrt 2$$
We can use the product rule for square roots to rewrite the two radicals as a single radical, a product of the two radicands: $$(\sqrt 5x)(\sqrt 10x) = \sqrt (5x\times10x)$$ We multiply the factors in the radicand to get: $$\sqrt 50x^2$$ $50x^2$ is the product of the perfect square $25x^2$ and $2$. $$\sqrt(50x^2) = \sqrt (25x^2) \sqrt 2$$ Since $25x^2$ is a perfect square, we can simplify this radical by taking the square root of $25x^2$, which is $5x$: $$5x\sqrt 2$$