Assume a and b are nonzero 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 answers.

Part A: ac + d

Question

Assume a and b are nonzero 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 answers.

Part A: ac + d

triciaal · Answer

@mathmate

nica3456 · Answer

Need Help with Part a but part b wont come up

mathmate · Answer

If you multiply a rational by an irrational, it will stay irrational.
Same goes for adding irrationals to rationals, and adding irrationals to irrationals.
Think of sqrt(2).  No matter how many times you add, or multiply, or divide, by rationals, you cannot get rid of the radical.
HOWEVER, multiplying two irrational $could$ end up with a rational.
Example: 
sqrt(2)*sqrt(3)=sqrt(6), still irrational
sqrt(2)*sqrt(8)=sqrt(16)=4, rational.

nica3456 · Answer

I don't understand if A or B is a rational or irrational