Find the answer to zero point 39 repeating plus square root of 175 end square root and select the correct answer below. also, is the sum of a nonzero rational number and an irrational number classified as rational or irrational?

You haven't shared the possible answer list.  But we can still "find the answer," whatever that means (you haven't defined your goal).

0.39 repeating  +  sqrt(175)

0.39 is rational; do you know how to find the equivalent numerical ratio?  It's 
         13/33.

On the other hand, 175 = 7*25.  7 is not a perfect square; 25 is one.
Thus, sqrt(175) = sqrt(25)*sqrt(7) = 5 sqrt(7).  sqrt(7) is irrational.

The sum of a rational expression and an irrational one is irrational.