# How do you simplify sqrt(49)/sqrt(500)?

Jan 29, 2016

$\frac{\sqrt{49}}{\sqrt{500}} = \frac{7}{10 \sqrt{5}} = \frac{7 \sqrt{5}}{50}$

#### Explanation:

We will use the following properties:

• If $a \ge 0$ then $\sqrt{{a}^{2}} = a$

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

$\frac{\sqrt{49}}{\sqrt{500}} = \frac{\sqrt{{7}^{2}}}{\sqrt{{10}^{2} \cdot 5}}$

$= \frac{7}{\sqrt{{10}^{2}} \sqrt{5}}$

$= \frac{7}{10 \sqrt{5}}$

We could finish here, or rationalize the denominator by multiplying the numerator and denominator by $\sqrt{5}$ to obtain

$\frac{7}{10 \sqrt{5}} = \frac{7 \sqrt{5}}{10 \sqrt{5} \sqrt{5}}$

$= \frac{7 \sqrt{5}}{10 \cdot 5}$

$= \frac{7 \sqrt{5}}{50}$