I am both a Mechanical and an Electrical engineer ( aka use math in real life every day) and I work every day with systems described by exponential or logarithmic functions. Just to name a few:...
Can you use trigonomic functions in real life situations? It's not like you carry a calculator with you everywhere...
Very unlikely unless you have a job that requires trig skills.
If you work in science or engineering, you will need radical functions (and other advanced math topics) all the time. Otherwise, you won't have much need for radical functions.