What is the distance between  (4,0)  and  (5,2) ?

$\sqrt{5}$
Let's say $A \left(4 , 0\right)$ and $B \left(5 , 2\right)$. The distance between those points is the norm of the vector $A B \left({x}_{b} - {x}_{a} , {y}_{b} - {y}_{a}\right) = \left(1 , 2\right)$.
The norm of a vector $u \left(x , y\right)$ is given by the formula $\sqrt{{x}^{2} + {y}^{2}}$.
So the norm of $A B$ is $\sqrt{{1}^{2} + {2}^{2}} = \sqrt{5}$ which is the distance between $A$ and $B$.