Which of the following correctly describes the sum of a rational number and an irrational number?

Question

which one a b c or d

 

always rational


 
both rational and irrational


 
can be either rational or irrational depending on the rationals used


 
always irrational

Answer 1

Hi Angel:

 

Always irrational. 

 

Proof by contradiction.  Suppose that the sum is rational. Then the DIFFERENCE between the one given rational number and the sum (assumed to be rational) is also RATIONAL.  But the difference is the original irrational number!  So, we arrive at a contradiction.  An irrational number can not be a rational number at the same time.  Done.

 

Dattaprabhakar (Dr. G.)