Solution
= Solution
For $n>0$,
$$
\frac{\sqrt{n^6+n^2}}{n^3}=\sqrt{1+n^{-4}}\longrightarrow1.
$$
Consequently $\boxed{\sqrt{n^6+n^2}=\Theta(n^3),\quad\text{in particular }O(n^3)}$ in <Big theta notation> and <Big O notation>.
= Solution
For $n>0$,
$$
\frac{\sqrt{n^6+n^2}}{n^3}=\sqrt{1+n^{-4}}\longrightarrow1.
$$
Consequently $\boxed{\sqrt{n^6+n^2}=\Theta(n^3),\quad\text{in particular }O(n^3)}$ in <Big theta notation> and <Big O notation>.