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

Answer

Let 2 +√3 be a rational number.

⇒ 2 +√3 = p/q; p, q ∈ I, q ≠ 0

⇒√3 = p/q – 2 = (p – 2q)/q

(p – 2q)/q is rational ⇒ √3 is rational number

which is a contradiction

(2 + √3) is an irrational number.

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