Since
![3^2=9,\quad 4^2=16](https://img.qammunity.org/2020/formulas/mathematics/college/olvk9zlqwviojaid2kwr5vvgvz7q78b5pd.png)
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
![\begin{array}cn&n^2\\3&9\\3.1&9.61\\3.2&10.24\\3.3&10.89\\3.4&11.56\end{array}\right]](https://img.qammunity.org/2020/formulas/mathematics/college/4ujj7vnkiw0a320tyy9n08gfvlc6txorwp.png)
So, the square root of 11 is somewhere between 3.3 and 3.4.