Question

2+√3 is an irrational no prove it

Answer 1

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HEY MATE HERE IS YOUR ANSWER--

let us assume 2+√3 as rational.

⇒2+√3=a/b

∴2-a/b=-√3 or √3=a/b-2

⇒√3=a/b-2

√3=a-2b/b

∵a and b are positive integers 

∴a-2b/b is rational

⇒√3 is rational

but we know that √3 is irrational 

∴⇒2+√3 is irrational

Answer 2

let 2-√3 be rational number

so, 2-√3=p/q

-√3=p/q-2

since A and B are integers a/b-2 is a rational no. and therefore -√3 is a rational number but this contradicts the fact that is a irrational number

this contradiction arises as we have assumed 2-√3 as a irrational number