A sum of two radicals is not a third radical

Proved

WorkbookSource.base_53335

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

lean-workbooksource-checked

Show that $\sqrt{11} + \sqrt{13} eq \sqrt{48}$ algebraically.

Source: InternLM Lean-Workbook, record lean_workbook_53335 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_53335 : ¬ (Real.sqrt 11 + Real.sqrt 13 = Real.sqrt 48)  :=  by sorry

Source