# How do you rationalize the denominator and simplify sqrt(49/10)?

Apr 6, 2016

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

#### Explanation:

color(blue)(sqrt(49/10)

Remember color(brown)(sqrt(x/y)=sqrtx/sqrty

So,

$\rightarrow \sqrt{\frac{49}{10}} = \frac{\sqrt{49}}{\sqrt{10}}$

$\rightarrow \frac{7}{\sqrt{10}}$

But wait!,In mathematics generally:

The denominators of fraction are not irrational numbers (the

numbers that cannot be expressed in the form $\frac{x}{y}$). So,we need to

rationalize the denominator.

So,

Multiply the whole fraction with

$\rightarrow \frac{7}{\sqrt{10}} \cdot \frac{\sqrt{10}}{\sqrt{10}}$

color(green)(rArr=(7sqrt10)/10