# How do you simplify sqrt(49-x^2)?

Jan 31, 2016

#### Answer:

This expression cannot be simplified, but it can be re-expressed:

$\sqrt{49 - {x}^{2}} = \sqrt{7 - x} \sqrt{7 + x}$

#### Explanation:

If $a \ge 0$ or $b \ge 0$ then $\sqrt{a b} = \sqrt{a} \sqrt{b}$

For any Real number $x$, at least one of $7 - x \ge 0$ or $7 + x \ge 0$, so we find:

$\sqrt{49 - {x}^{2}} = \sqrt{\left(7 - x\right) \left(7 + x\right)} = \sqrt{7 - x} \sqrt{7 + x}$