How do you rationalize the denominator and simplify sqrt (1 / 3)?

Apr 9, 2018

$\frac{\sqrt{3}}{3}$

Explanation:

law of surds:

$\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$

here, $\sqrt{\frac{a}{b}} = \sqrt{\frac{1}{3}}$.

using this law, $\sqrt{\frac{1}{3}}$ is the same as $\frac{\sqrt{1}}{\sqrt{3}}$.

$\sqrt{1}$ is $1$, so $\sqrt{\frac{1}{3}}$ is the same as $\frac{1}{\sqrt{3}}$.

the denominator can be rationalised by multiplying both the numerator and the denominator by $\sqrt{3}$.

$1 \cdot \sqrt{3} = \sqrt{3}$

$\sqrt{3} \cdot \sqrt{3} = 3$

$\frac{1}{\sqrt{3}} = \frac{1 \cdot \sqrt{3}}{\sqrt{3} \cdot \sqrt{3}}$

$= \frac{\sqrt{3}}{3}$