Question

Prove that 2-√3 is irrational, given that
√3 is irrational​

Answer 1

Question

Prove that 2-√3 is irrational, given that

√3 is irrational​

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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