# Question 28264: Real Domain of the Principal Square Root

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This teaching derivation has second-context AI mathematical and bilingual semantic review, limited to the model and assumptions stated in this question. It has no human review or new Lean proof and does not promote the original question or MKO to Canonical truth.

R0055-28264 · q-20261003-r01-power-root-0089



## Original question and givens

The real principal square root in this exercise is defined only for nonnegative inputs. Does r=1 belong to its domain? Answer Yes or No.


- G001 — The real principal square root in this exercise is defined only for nonnegative inputs. Does r=1 belong to its domain? Answer Yes or No.





## Definition and scope

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.


- [mko-power-root](https://ocme.evemisslab.com/en/mko/mko-power-root/)





## Step-by-step derivation

S001 · impliesBefore

source roles = [qf-principal-square-root-domain, sqrt_domain]

After

derived = [[real_principal_root_domain_yes_no]]

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.

Step identifiers and dependenciesRule: source_answer_roles_or_ordered_fields_without_JS · Uses: G001





S002 · impliesBefore

source roles = [1]

After

derived = [Yes, Yes]

Conditions: none

The real principal-root domain is r>=0.A negative input receives only a domainNo,not0 or a substituted complex branch.

Step identifiers and dependenciesRule: Legacy_real_principal_root_domain_negative_NO_assigned_root · Uses: G001, S001









## Reverse checks


- S002 · premise_and_result_audit — Reverse-check complete original data,operands and premises;finite checks,conditional reasoning,formal proof and publication authority remain distinct.
- S001 · premise_and_result_audit — Reverse-check complete original data,operands and premises;finite checks,conditional reasoning,formal proof and publication authority remain distinct.





## Result

Yes

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.





## This question review and source binding

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.

Source hashes and review receipts
- input commit: 0f7be61e2c22317a4075561dc822c87d881a50db
- original question SHA-256: 7cf0c11d25c57ba339670f9b75a4efdd502da1f3bc6833d3c6fe6d8ccd2842a1
- candidate record SHA-256: 46179f626966b0c1ddfb0394cf321b19667278d03c78b27c7afdd7a7ee0fa980
- semantic review receipt SHA-256: 6af367dae24a584f3596525c4953bbc2115343efd68cc9083693eb5c1ef2e683
- question-first witness SHA-256: 611eb69f3716404b968296a8b0d7d8c61b5ca18129d406f1ff9c7c11e10ffb4e
- Lean: NOT_RUN · human review: NOT_PERFORMED

[Same-source full JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261003-r01-power-root-0089.json)