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.

Two vector spaces over the same field (in our case $\mathbb Q$) are isomorphic if and only if they have the dimension (this also holds for infinite dimensional vector spaces). Now it is left to show that the $\mathbb Q$ vector space $\mathbb R$ has dimension $|\mathbb R|$. Then you immediately get that the dimension of $\mathbb R^n$ is the same since $\mathbb R$ is a subspace of $\mathbb R^n$ and the dimension is bounded by the number of elements $|\mathbb R^n|=|\mathbb R|$.
