# What is the domain of sqrt(x^2-9)?

##### 1 Answer
Oct 11, 2016

The domain of this expression is {x|x < -3 or x > 3}.

#### Explanation:

To find restrictions to the domain of a square root expression, you must determine which values of the variable will make the radicand have a negative value.

${x}^{2} - 9 < 0$
${x}^{2} - 9 + 9 < 0 + 9$
${x}^{2} < 9$
${\sqrt{x}}^{2} < \sqrt{9}$
$x < \pm 3$

This actually tells us that $x$ cannot be between $- 3$ and $3$, inclusive. Therefore $x$ must be less than $- 3$ or greater than $3$.