Question

If a is a non zero rational and √b is irrational then a√b is *



rational

irrational

real but rational

not confirmed

​

Answer 1

Step-by-step explanation:

let us assume on the contrary that a?b is rational. then there exist co-prime integers x and y such that,

this implies, a?b=x/y

this implies, ?b=x/ay

this implies, ?b is rational [therefore,a,x and y are integers then x/ay is a rational number]

this contradicts the fact that ?b is rational no.. so our assumption is not correct.

hence a?b is an irrational number