6. Prove v3+2 +1 is irrational. – InterviewSolution

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6. Prove v3+2 +1 is irrational.

Answer»

Let √3 + √2 + 1 be rational

√3 + √ 2 + 1 = r , r be any rational

sqauring both sides

(√3 + √2)² = (r - 1)²

3 + 2 + 2 √6 = r² - 2r + 1

√6 = (r² - 2r - 4)/2

So, contradiction to our assumption as LHS is irrational and RHS is rational.

So, √3 + √2 + 2 is irrational

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