Since
[tex]3^2=9,\quad 4^2=16[/tex]
The square root of 11 is somewhere between 3 and 4. In order to round it to the nearest tenth, we have to try all numbers between 3 and 4 with one decimal digit, and see which is closest to 11 when squared. We have
[tex]\begin{array}{c|c}n&n^2\\3&9\\3.1&9.61\\3.2&10.24\\3.3&10.89\\3.4&11.56\end{array}\right][/tex]
So, the square root of 11 is somewhere between 3.3 and 3.4.
