# How do you find the square root of 92/207?

Feb 5, 2017

$\sqrt{\frac{92}{207}} = \frac{2}{3}$

#### Explanation:

First check the prime factorisations of the numerator and denominator to see what square factors there are:

$92 = 2 \cdot 2 \cdot 23$

$207 = 3 \cdot 3 \cdot 23$

So:

$\sqrt{\frac{92}{207}} = \sqrt{\frac{{2}^{2} \cdot \textcolor{red}{\cancel{\textcolor{b l a c k}{23}}}}{{3}^{2} \cdot \textcolor{red}{\cancel{\textcolor{b l a c k}{23}}}}} = \frac{2}{3}$

Note that $\frac{92}{207}$ has another square root, namely $- \frac{2}{3}$, but I follow the common usage here that "the" square root means the non-negative one.