Question

Given that √3 is an irrational number prove that (2+√3) is an irrational number

Answer 1

Answer:

2+root3 is an irrational no

because root 3 is given as irational

Step-by-step explanation:

Answer 2

Step-by-step explanation:

let us assume, to the contrary that 2+root 3 is rational.

that is, we can find coprime a and b (b not equal to 0) such that 2+root3 =a/b

therefore 2+a/b=root 3

rearranging this equation, we get root 3=2+a/b=2b+a upon b

since a and b are integers, we get 2+a/b is rational and so root 3 is rational

but this contradicts the fact that root 3 is irrational.

this contradiction has arisen because of our incorrect assumption that 2+root 3 is rational

so 2+root 3 is irrational