lean_workbook_plus_53271

⚠️ Retired — specification defect

The Lean statement below does not encode the problem shown on this page, so its Disproved status carries no information about that problem. Do not import this node or use it as a dependency.

Simplify $(\sqrt{5} + \sqrt{3})^6$ without actually calculating each term of the series using the binomial formula.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_53271 : (5^(1/2) + 3^(1/2))^6 = 27 + 125 + 150 + 50 + 12 + 2   :=  by sorry

Fractional-looking exponents elaborate as natural-number quotients, changing roots to powers0 (or another integer).

The recorded counterexample refutes the statement as encoded. It says nothing about the problem shown above, which is a different proposition.

Confirmed directly from the Lean text: the numeric-literal exponent carries no type ascription, so it elaborates at type ℕ where division truncates (^(1/2) → ^0).

Proposed corrected statement

Use genuine real roots and explicitly real fractional exponents. For odd roots of negative values use the signed real root. Retain the source domain and verify the repaired claim rather than infer its truth from this counterexample. Original task: Simplify $(\sqrt{5} + \sqrt{3})^6$ without actually calculating each term of the series using the binomial formula. The inserted finite integer answer is not recovered; compute the genuine radical expression instead.

Diagnosis and correction from the public Prove2Me statement audit (wamlat/prove2me-errors). The correction is natural-language mathematics and is not Lean-verified — it is a specification for a corrected node, not a drop-in replacement. No corrected replacement node exists yet.