How can I solve this integer part question?

Question

I am trying to understand this problem but my textbook does not offer a good explanation,it asks what the integer part of the square root is.

$\sqrt{n^2+6n}$ , $n \in N$*

Answer 1

The integer part of the square root is what you would get if you performed the root operation normally and then chopped off the decimal digits, leaving behind an integer.

For $n\ge2$, $$(n+2)^2=n^2+4n+4\le n^2+6n<n^2+6n+9=(n+3)^2$$ So the integer part is $n+2$ if $n\ge2$. (For $n=1$ the integer part is $2$.)