Prove that as a $\Bbb Q$ vector space $\Bbb R^n$ is isomorphic to $\Bbb R$ 
Prove that as a $\mathbb{Q}$ vector space, $\mathbb{R}^n$ is isomorphic to $\mathbb{R}.$

I came across this statement somewhere and I have been trying to prove it ever since, but I just don't know how to start or what to define as the map.

You can use the statements that both $\Bbb R$ and $\Bbb R^n$ are infinite (uncountable) dimensional extensions over $\Bbb Q$ and two vector spaces of same dimension are isomorphic. And $|\Bbb Q| < |\Bbb R|$. So $dim(\Bbb R)= |\Bbb R|= |\Bbb R^n|=dim(\Bbb R^n)$.
