How do you simplify #sqrt(9)#?

1 Answer
Jul 14, 2015

Answer:

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.