Question

If a is rational and sqrt(b) is irrational then prove that (a+sqrt(b)) is irrational.

Answer 1

Answer:

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.

Answer 2

Answer:

Please Find the answer in the above picture .