# How do you simplify sqrt(49/121)?

$\sqrt{\frac{49}{121}} = \frac{\sqrt{49}}{\sqrt{121}} = \frac{\sqrt{{7}^{2}}}{\sqrt{{11}^{2}}} = \frac{7}{11}$
For any $x \ge 0$, $\sqrt{{x}^{2}} = x$, by the definition of square roots.
Also, $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$ for any $a \ge 0$ and $b > 0$.