# How do you simplify sqrt(9)?

Jul 14, 2015

3

#### Explanation:

For a given real number $a \setminus \ge q 0$, the symbol $\setminus \sqrt{a}$ represents the unique non-negative real number whose square is $a$. That is, ${\left(\setminus \sqrt{a}\right)}^{2} = a$.

Since ${3}^{2} = 9$ it follows that $\setminus \sqrt{9} = 3$.

Proving that $\setminus \sqrt{a}$ exists and is unique in the general situation mentioned above from the foundations of arithmetic is actually no easy feat. Take real analysis someday if you want to learn more.