Question

prove that the sum of a rational no. and an irrational no. is alwaysan 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 )