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