Question

How do you simplify `sqrt(9)`?

Answer 1

3

Explanation:

For a given real number `a\geq 0`, the symbol `\sqrt{a}` represents the unique non-negative real number whose square is `a`. That is, `(\sqrt{a})^{2}=a`.

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

Proving that `\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.