Prove that $|\mathbb R^n | = |\mathbb R|$.

Question

Prove that $|\mathbb{R}^n| = |\mathbb{R}|$.

It will be enough to prove $|\mathbb{R}^{2}|=|\mathbb{R}|$. We can further simplify by proving $|(0,1)\times(0,1)| = |(0,1)|$ (because $|\mathbb{R}|=|(0,1)|$).

BUT how to proceed further?