# What is the square root of 144/169?

Mar 2, 2018

$\frac{12}{13}$ or $0.923$

#### Explanation:

We can write this as:

$\sqrt{\frac{144}{169}}$

This is the same thing as taking the square root of the numerator and the denominator, then dividing:

$\frac{\sqrt{144}}{\sqrt{169}}$

Square root of $144 = 12$
Square root of $169 = 13$

$= \frac{12}{13}$

In decimals, it is:

$\approx 0.923$

Thus, we have our answer.

Mar 2, 2018

$\textcolor{b l u e}{\pm \frac{12}{13}}$

#### Explanation:

$\sqrt{\frac{144}{169}}$

$\sqrt{\frac{{12}^{2}}{{13}^{2}}}$

$\textcolor{red}{\frac{12}{13}}$

Or

$\sqrt{\frac{{\left(- 12\right)}^{2}}{{13}^{2}}}$

$\textcolor{red}{\frac{- 12}{13}}$

Or

$\sqrt{\frac{{12}^{2}}{{\left(- 13\right)}^{2}}}$

$\frac{12}{- 13}$

$\textcolor{red}{\frac{- 12}{13}}$

Or

$\sqrt{\frac{{\left(- 12\right)}^{2}}{{\left(- 13\right)}^{2}}}$

$\frac{- 12}{- 13}$

$\textcolor{red}{\frac{12}{13}}$