lean_workbook_plus_34023

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Let $n$ be a positive integer. Prove that at least two numbers of $\sqrt{n},\ \sqrt{n+1},\ \sqrt{n+2}$ are irrational numbers.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_34023 (n : ℕ) (hn : 0 < n) : ∃ k : Fin 3, ¬ ∃ a : ℚ, (k : ℝ) = √(n + k)   :=  by sorry

Source