Question

Prove that 2+√3 is irrational.


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Answer 1

Answer:

sum of rational numbers and irrational numbers is irrational

Answer 2

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

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