Question

Prove that the sum of a rational number and an irrational number is an irrational number.

Answer 1

Let  rational number +  irrational number  = rational number

And we know " rational number can be expressed in the form of  pq , where p , q are any integers And q ≠ 0 , 
So, we can expressed our assumption As :

pq + x  = ab                                  ( Here x is a irrational number )

x = ab   -  pq 
So,

x is a rational number , but that contradict our starting assumption . 
Hence

rational number +  irrational number  = irrational number                       ( hence proved )