Prove this inequality $3^{n}\geq n^{2}$ for $n\geq 1$ with mathematical induction.

**Base step**: When $n=1$

$3^{1}\geq1^{2}$, statement is true. 

**Inductive step**: We need to prove that this statement $3^{n+1}\geq (n+1)^{2}$ is true. 

So, to get the left side of this statement is easy. We can get it by multiplying $3^{n}\geq n^{2}$ with $3$.

After this step we have $3^{n+1}\geq 3n^{2}$.

What we now have to get is the right side and we can transform it like this:

$3n^{2}= (n^{2}+2n+1)+(2n^{2}-2n-1)$ which is same as

$(n+1)^{2}+(2n^{2}-2n-1)$.

So now we have $(n+1)^{2}$ and $(2n^{2}-2n-1)$ and my question is how should i use this to prove inequality?