$$For each of the examples below, state why an approximated solution is a reasonable choice:

a$.$ For computing the value of $$

Due to the irrational nature of the number itself, an approximation is reasonable and the fact that exact values are impractical for most applications further proves an approximation is suitable.

b$.$ For a machine learning algorithm based on decision trees

$$

c$.$ For the traveling salesperson problem

d$.$ For a strategy game available on a mobile device

Hint: if your reasons are based on the problem$$s nature, specify what is that nature with respect to the approximated solution; if you think that an approximated solution is not reasonable for the problem, state why.