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R0055-28276 · q-20261003-r01-power-root-0051
Using the principal square root on the nonnegative reals, find the exact nonnegative value of √0.
G001 — Using the principal square root on the nonnegative reals, find the exact nonnegative value of √0.Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.
Before
source roles = [qf-principal-square-root-exact, principal_sqrt]
After
derived = [[single_nonnegative_exact_integer_root]]
Conditions: none
List this scalar/label/set/point answer role or mode-specific ordered fields,not an imposed universal tuple.Retain legacy domain/underscore operation and integer fractions with/1;original bilingual snapshots stay unchanged.
Rule: source_answer_roles_or_ordered_fields_without_JS · Uses: G001
Before
Legacy principal ORIGINAL radicand terminal root square := mul(0, 0)
After
Legacy principal ORIGINAL radicand terminal root square = 0
Conditions: none
Substitute original roles exactly,without floating approximation or changed operands;extra teaching identities add no source-domain restrictions.
Rule: exact_rational_arithmetic · Uses: G001, S001
Before
Legacy principal ORIGINAL radicand terminal successor square := mul(1, 1)
After
Legacy principal ORIGINAL radicand terminal successor square = 1
Conditions: none
Substitute original roles exactly,without floating approximation or changed operands;extra teaching identities add no source-domain restrictions.
Rule: exact_rational_arithmetic · Uses: G001, S002
Before
source roles = [Legacy principal ORIGINAL radicand, 0, 0, 1]
After
derived = [0, 1]
Conditions: none
Adjacent integer bounds certify floor sqrt=low;an exact root separately needs low²=n,and the principal root is the single nonnegative branch.
Rule: Legacy_isqrt_terminal_floor_and_single_nonnegative_branch · Uses: G001, S003
Before
source roles = [0]
After
derived = [0, Yes]
Conditions: none
Check root²=r and root>=0.Monotonicity of nonnegative squaring gives uniqueness;two signed equation roots are not the principal-root value.
Rule: Legacy_PERFECT_square_exact_NONNEGATIVE_principal_root · Uses: G001, S004
S005 · premise_and_result_audit — Reverse-check complete original data,operands and premises;finite checks,conditional reasoning,formal proof and publication authority remain distinct.S004 · premise_and_result_audit — Reverse-check complete original data,operands and premises;finite checks,conditional reasoning,formal proof and publication authority remain distinct.S003 · premise_and_result_audit — Recompute Legacy principal ORIGINAL radicand terminal successor square with exact rational arithmetic, not rounded decimals.S002 · premise_and_result_audit — Recompute Legacy principal ORIGINAL radicand terminal root square with exact rational arithmetic, not rounded decimals.S001 · premise_and_result_audit — Reverse-check complete original data,operands and premises;finite checks,conditional reasoning,formal proof and publication authority remain distinct.0
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
Review date: 2026-10-26
Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.
input commit: 0f7be61e2c22317a4075561dc822c87d881a50dboriginal question SHA-256: 5a7c9d0993b9a5facc5a34dea9efd1b351f4565d094a1a6f8d80fa1369baefb1candidate record SHA-256: 025ee6baa48942a6f81fb218a2b404676bc7555c77d4f226551880adf8833c81semantic review receipt SHA-256: 6af367dae24a584f3596525c4953bbc2115343efd68cc9083693eb5c1ef2e683question-first witness SHA-256: 611eb69f3716404b968296a8b0d7d8c61b5ca18129d406f1ff9c7c11e10ffb4eLean: NOT_RUN · human review: NOT_PERFORMED