In which way to prove that the set has the measure zero in R3?

Question

I can understand this task in the way that we should prove that there are less numbers in the rational set compared to the numbers in the real set ?

TO PROVE:

The set A is described as follows:

$A=\{(x,y,z)\in\mathbb{R}^3 : 0 \leq x \leq 1,0\leq y \leq 1, 0\leq z\leq 1,x \in \mathbb{Q}\}$

I've looked the theory for "measure" and the number of real ($\mathbb{R}$) and rational ($\mathbb{Q}$) numbers. And then?