A strict square-root bound

Proved

WorkbookSource.problem_53725

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Given $n > \frac{25}{12}$ , prove that $\sqrt{n(n+2)} > n + \frac{5}{6}$

Source: InternLM Lean-Workbook, record lean_workbook_53725 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved.

Preamble

import Mathlib
open Real

Formal statement

theorem WorkbookSource.problem_53725 (n : ℝ) (h : n > 25 / 12) : Real.sqrt (n * (n + 2)) > n + 5 / 6  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_53725; Apache-2.0

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