Is $\mathbb{R}^2 \setminus \mathbb{Q}^2$ Homeomorphic To $\mathbb{R} \setminus \mathbb{Q}$ ?

Let $\mathbb{R}^2 \setminus \mathbb{Q}^2$ denote the Cartesian plane minus all points whose coordinates are both rational. Similarly, let $\mathbb{R} \setminus \mathbb{Q}$ denote the irrational numbers. Are the spaces $\mathbb{R}^2 \setminus \mathbb{Q}^2$ and $\mathbb{R} \setminus \mathbb{Q}$ homeomorphic?

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Hint : Is $\mathbb{R}^2 \setminus \mathbb{Q}^2$ path-connected?