Question

prove that product of a rational and irrational number is irrational ​

Answer 1

Answer:

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Answer 2

Answer:

let x be a non zero rational no. and y be an irrational no. then then we have to show that xy is an irrational no. if possible let xy be rational no. since quotient of two non zero rational no. is always a ratonal no.

therefore, xy is a rational no and x is a rational no.

-> [xy/x] is arational no.

-> y is a rational no.

but, this cntradicts the fact that y is an irrational no. thus,our supposition is wrong

hence, xy isa rational no.