Between which integers is $-3 + \sqrt 5$ situated? I can't understand how to solve this question . I'll be thankful if you help me. Please solve it and post your complete solution & a little description of what you did. > Between which integers is $-3 + \sqrt 5$ situated? Sorry for my bad English

Another take.

Notice that $$-3+\sqrt4\lt-3+\sqrt5\lt-3+\sqrt9\Rightarrow\\\\-1\lt-3+\sqrt5\lt0$$

Since $$|0-(-1)|=1$$ is the smallest distance between two (different) integers, this is the required interval.