Assume a and b are rational numbers and c and d are irrational numbers for each of the following expressions determine whether the result is irrational rational or both. justify your answer.
part a: ac + d
part b: 4b root 3 + c
part c: b^2 (c+d)

Part A: ac + d  the result is irrational number 
proof,
the product of irrational number with any number apart from 0 is an irrational number

Part B: 4b root 3 + c
 the result is irrational number,           
proof
root 3 is an irrational number, the product and sum of irrational number with any number apart from 0 is an irrational number

Part C: b^2 (c+d)  bthe result is irrational
proof
c+d is an irrational number, b² is rational number, so the result of the product is an irrational number