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

For $\sqrt{x^2+2}$ to be a real number, $x^2+2$ must be non-negative. $x^2+2\geq0$ Subtract 2 from both sides of the inequality and simplify. $x^2+2-2\geq0-2$ $x^2\geq-2$ Since $x^2$ is always non-negative, the expression is true for all real number values of x.