# What is the square root of 1/3?

Mar 22, 2018

$\approx 0.577$

#### Explanation:

$\sqrt{\frac{1}{3}} = \frac{1}{\sqrt{3}} \approx 0.577$

Mar 22, 2018

The square root of $\frac{1}{3}$ is an irrational number that can be written as $\textcolor{b l u e}{\frac{1}{\sqrt{3}}}$

#### Explanation:

You could use a calculator to find the approximate value of this, namely $0.5773502692$ (but since $\frac{1}{\sqrt{3}}$ is irrational, this is not exact).

Mar 22, 2018

The square root of $\frac{1}{3}$ is $\frac{\sqrt{3}}{3}$ $\approx 0.577$.

#### Explanation:

When you square root a fraction, you square root both the numerator and the denominator.
$\sqrt{\frac{1}{3}}$
$= \frac{\sqrt{1}}{\sqrt{3}}$
$= \frac{1}{\sqrt{3}}$
$= \frac{\sqrt{3}}{3}$

Mar 22, 2018

See below

#### Explanation:

If you want to find $\sqrt{\frac{1}{3}}$ yu must use the power laws.

$\sqrt{\frac{1}{3}} = \frac{\sqrt{1}}{\sqrt{3}} = \frac{1}{\sqrt{3}}$. We have to rationalize this fraction (remove square roots in denominator)

Multipliying by $\sqrt{3}$ in numerator and denominator, we have

1/sqrt3=(1·sqrt3) /(sqrt3·sqrt3)=sqrt3/3