{"ok":true,"question":{"id":21039,"question_uuid":"8a521bf6-d82a-46ef-999d-7dcdbfa41586","job_id":3,"source_file":"人教版/七下/2026江苏七年级期末数学试卷+答案385.pdf","source_page_start":2,"source_page_end":2,"source_bbox":"[304.5, 378.0, 480.08, 425.8]","subject_code":"math","grade_level":"SENIOR","tree_code":"KT_SENIOR_MATH_STANDARD","question_type":"comprehensive","canonical_json":"{\"year\": null, \"blocks\": [{\"text\": \"求下列各数的立方根：\", \"type\": \"text\"}, {\"type\": \"subquestion\", \"index\": 1, \"blocks\": [{\"text\": \"− 0.027;(2)\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"3\\\\frac{3}{8}\"}, {\"text\": \"(3) −\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\frac{343}{512}\"}, {\"text\": \"(4)(−5)3\", \"type\": \"text\"}]}, {\"type\": \"solution\", \"blocks\": [{\"text\": \"(1)^{3}\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\sqrt{−0.027} = 3 \\\\sqrt{(−0.3)^{3}} =\"}, {\"text\": \"−0.3 (2)因为\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"3\\\\frac{3}{8} = \\\\frac{27}{8},(\\\\frac{3}{2})3 = \\\\frac{27}{8}\"}, {\"text\": \"所以\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\frac{27}{8}\"}, {\"text\": \"的立方 根是\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\frac{3}{2}\"}, {\"text\": \"即\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"3 \\\\sqrt{383} = \\\\frac{3}{2}\"}, {\"text\": \". (3)因为(-\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\frac{7}{8}\"}, {\"text\": \")3 = −\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\frac{343}{512}\"}, {\"text\": \"，所以−\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\frac{343}{512}\"}, {\"text\": \"的立方根 是 −\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\frac{7}{8}\"}, {\"text\": \"即\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"3 \\\\sqrt{−512343} =\"}, {\"text\": \"− 7 . 8 （）4(−5)3的立方根是 − 5,即\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"3 \\\\sqrt{(−5)^{3}} =\"}, {\"text\": \"−5．\", \"type\": \"text\"}]}], \"source\": {\"bbox\": [304.5, 378.0, 480.08, 425.8], \"file\": \"人教版/七下/2026江苏七年级期末数学试卷+答案385.pdf\", \"regions\": [{\"bbox\": [304.5, 378.0, 480.08, 425.8], \"page\": 2}], \"section\": \"example\", \"page_end\": 2, \"page_start\": 2, \"section_label\": \"跟我学        关键母题，常考题型各个击破！\", \"answer_regions\": [{\"bbox\": [298.12841796875, 518.5242309570312, 526.1517333984375, 692.2554931640625], \"page\": 2}], \"answer_original\": \"\", \"solution_original\": \"(1)^{3} \\\\sqrt{−0.027} = 3 \\\\sqrt{(−0.3)^{3}} = −0.3 (2)因为3\\\\frac{3}{8} = \\\\frac{27}{8},(\\\\frac{3}{2})3 = \\\\frac{27}{8},所以 \\\\frac{27}{8}的立方 根是 \\\\frac{3}{2},即3 \\\\sqrt{383} = \\\\frac{3}{2}. (3)因为(- \\\\frac{7}{8})3 = − \\\\frac{343}{512}，所以− \\\\frac{343}{512}的立方根 是 − \\\\frac{7}{8},即3 \\\\sqrt{−512343} = − 7 . 8 （）4(−5)3的立方根是 − 5,即3 \\\\sqrt{(−5)^{3}} = −5．\"}, \"version\": 1, \"grade_level\": \"SENIOR\", \"number_label\": \"2\", \"subject_code\": \"math\", \"question_type\": \"comprehensive\", \"content_sha256\": \"256ac3c2fdc75b685f41c4c8cf860b5abc52c75c1787c21ecb27f7f31b92508b\"}","body_html":"<div>求下列各数的立方根：<br>（1）− 0.027;(2)\\(3\\frac{3}{8}\\)(3) −\\(\\frac{343}{512}\\)(4)(−5)3</div>","answer_html":"","ways_html":"(1)^{3}\\(\\sqrt{−0.027} = 3 \\sqrt{(−0.3)^{3}} =\\)−0.3 (2)因为\\(3\\frac{3}{8} = \\frac{27}{8},(\\frac{3}{2})3 = \\frac{27}{8}\\)所以\\(\\frac{27}{8}\\)的立方 根是\\(\\frac{3}{2}\\)即\\(3 \\sqrt{383} = \\frac{3}{2}\\). (3)因为(-\\(\\frac{7}{8}\\))3 = −\\(\\frac{343}{512}\\)，所以−\\(\\frac{343}{512}\\)的立方根 是 −\\(\\frac{7}{8}\\)即\\(3 \\sqrt{−512343} =\\)− 7 . 8 （）4(−5)3的立方根是 − 5,即\\(3 \\sqrt{(−5)^{3}} =\\)−5．","explain_html":null,"difficulty":2,"score":null,"year":null,"parse_status":"PARSED","qa_status":"QUARANTINED","retry_count":0,"final_score":0.775,"error_message":"QA failed: VISION,COHERENCE,ANSWER","published_question_id":null,"content_sha256":"256ac3c2fdc75b685f41c4c8cf860b5abc52c75c1787c21ecb27f7f31b92508b","created_at":"2026-09-24T21:49:40","updated_at":"2026-09-24T22:07:49","answer_missing":true,"formula_fallback":false,"_number":"2","_section":"example","_section_label":"跟我学        关键母题，常考题型各个击破！"},"assets":[],"knowledge":[],"audits":[{"id":413426,"import_question_id":21039,"audit_type":"STRUCTURE","auditor_name":"structure-auditor","status":"PASS","score":1.0,"input_snapshot":"求下列各数的立方根： (1) − 0.027;(2) 3\\frac{3}{8} (3) − \\frac{343}{512} (4)(−5)3","result_json":"{\"ok\": true, \"issues\": [], \"confidence\": 1.0}","created_at":"2026-09-24T22:03:23"},{"id":413427,"import_question_id":21039,"audit_type":"FORMULA","auditor_name":"formula-auditor","status":"PASS","score":1.0,"input_snapshot":"3\\frac{3}{8}; \\frac{343}{512}; \\sqrt{−0.027} = 3 \\sqrt{(−0.3)^{3}} =; 3\\frac{3}{8} = \\frac{27}{8},(\\frac{3}{2})3 = \\frac{27}{8}; \\frac{27}{8}","result_json":"{\"risky\": 13, \"issues\": [], \"checked\": 13, \"invalid\": 0, \"visual_check\": \"delegated_to_question_vision\", \"invalid_details\": [], \"visually_verified\": 0}","created_at":"2026-09-24T22:03:23"},{"id":413428,"import_question_id":21039,"audit_type":"KNOWLEDGE","auditor_name":"knowledge-auditor","status":"WARN","score":0.0,"input_snapshot":"求下列各数的立方根： (1) − 0.027;(2) 3\\frac{3}{8} (3) − \\frac{343}{512} (4)(−5)3","result_json":"{\"picks\": [], \"tree_code\": \"KT_SENIOR_MATH_STANDARD\", \"candidates\": 0, \"classifier_version\": null}","created_at":"2026-09-24T22:03:23"},{"id":413441,"import_question_id":21039,"audit_type":"VISION","auditor_name":"vision-auditor","status":"WARN","score":0.2,"input_snapshot":"题干：\n求下列各数的立方根： （1）− 0.027;(2)\\(3\\frac{3}{8}\\)(3) −\\(\\frac{343}{512}\\)(4)(−5)3\n答案：\n\n解析：\n(1)^{3}\\(\\sqrt{−0.027} = 3 \\sqrt{(−0.3)^{3}} =\\)−0.3 (2)因为\\(3\\frac{3}{8} = \\frac{27}{8},(\\frac{3}{2})3 = \\frac{27}{8}\\)所以\\(\\frac{27}{8}\\)的立方 根是\\(\\frac{3}{2}\\)即\\(3 \\sqrt{383} = \\frac{3}{2}\\). (3)因为(-\\(\\frac{7}{8}\\))3 = −\\(\\frac{343}{512}\\)，所以−\\(\\frac{343}{512}\\)的立方根 是 −\\(\\frac{7}{8}\\)即\\(3 \\sqrt{−512343} =\\)− 7 . 8 （）4(−5)3的立方根是 − 5,即\\(3 \\sqrt{(−5)^{3}} =\\)−5．","result_json":"{\"note\": \"视觉比对不可用\", \"error\": \"invalid_json\", \"unavailable\": true}","created_at":"2026-09-24T22:04:19"},{"id":413812,"import_question_id":21039,"audit_type":"SOLVER","auditor_name":"blind-solver","status":"PASS","score":1.0,"input_snapshot":"求下列各数的立方根： (1) − 0.027;(2) 3\\frac{3}{8} (3) − \\frac{343}{512} (4)(−5)3","result_json":"{\"basis\": \"立方根定义：若 x³ = a，则 x 是 a 的立方根。\\n(1) (-0.3)³ = -0.027 → 立方根为 -0.3\\n(2) (3/2)³ = 27/8 = 3.375 = 3又3/8 → 立方根为 3/2\\n(3) (-7/8)³ = -343/512 → 立方根为 -7/8\\n(4) (-5)³ = -125，所以 (-5)³ 的立方根是 -5\", \"answer\": \"(1) -0.3\\n(2) 3/2\\n(3) -7/8\\n(4) -5\", \"confidence\": 1.0, \"handout_chars\": 0}","created_at":"2026-09-24T22:06:16"},{"id":413813,"import_question_id":21039,"audit_type":"CRITIC","auditor_name":"critic","status":"PASS","score":1.0,"input_snapshot":"来源答案: || 盲解:(1) -0.3\n(2) 3/2\n(3) -7/8\n(4) -5","result_json":"{\"ok\": true, \"issues\": [], \"merged\": true, \"confidence\": 1.0}","created_at":"2026-09-24T22:06:16"},{"id":413814,"import_question_id":21039,"audit_type":"SYMBOLIC","auditor_name":"symbolic-auditor","status":"WARN","score":0.5,"input_snapshot":"答案: || 盲解:(1) -0.3\n(2) 3/2\n(3) -7/8\n(4) -5","result_json":"{\"checks\": [], \"detail\": {\"reason\": \"未提取到来源答案\"}, \"status\": \"WARN\", \"applicable\": true}","created_at":"2026-09-24T22:06:16"},{"id":413843,"import_question_id":21039,"audit_type":"COHERENCE","auditor_name":"coherence-auditor","status":"FAIL","score":0.9,"input_snapshot":"答案: || 解析:(1)^{3}\\(\\sqrt{−0.027} = 3 \\sqrt{(−0.3)^{3}} =\\)−0.3 (2)因为\\(3\\frac{3}{8} = \\frac{27}{8},(\\frac{3}{2})3 = \\frac{27}{8}\\)所以\\(\\frac{27}{8}\\)的立方 根是\\(\\frac{3}{2}\\)即\\(3 \\sqrt{383} = \\frac{3}{2}\\). (3)因为(-\\(","result_json":"{\"ok\": false, \"which\": [\"solution\"], \"issues\": [\"第 (2) 问中，带分数 3\\\\frac{3}{8} 被错误地写成 383，导致后续立方根表达式错误。\", \"第 (3) 问中，立方根结果 -\\\\frac{7}{8} 被误写为 -7.8，且表达式中分子分母顺序颠倒。\", \"3\\\\sqrt{383} = \\\\frac{3}{2}: 原文将 3\\\\frac{3}{8} 误写为 383，导致立方根表达式错误。正确应为 3\\\\sqrt{\\\\frac{27}{8}} = \\\\frac{3}{2}。\", \"3\\\\sqrt{-512343} = -7.8: 原文将 -\\\\frac{343}{512} 的立方根结果误写为 -7.8，且表达式中数字顺序混乱。正确结果应为 -\\\\frac{7}{8}。\"], \"confidence\": 0.9, \"equation_checks\": [{\"valid\": false, \"reason\": \"原文将 3\\\\frac{3}{8} 误写为 383，导致立方根表达式错误。正确应为 3\\\\sqrt{\\\\frac{27}{8}} = \\\\frac{3}{2}。\", \"equation\": \"3\\\\sqrt{383} = \\\\frac{3}{2}\"}, {\"valid\": false, \"reason\": \"原文将 -\\\\frac{343}{512} 的立方根结果误写为 -7.8，且表达式中数字顺序混乱。正确结果应为 -\\\\frac{7}{8}。\", \"equation\": \"3\\\\sqrt{-512343} = -7.8\"}]}","created_at":"2026-09-24T22:07:49"},{"id":413844,"import_question_id":21039,"audit_type":"QUALITY_GATE","auditor_name":"quality-gate","status":"FAIL","score":0.775,"input_snapshot":"","result_json":"{\"warnings\": [], \"graded_gate\": true, \"hard_failed\": [\"VISION\", \"COHERENCE\", \"ANSWER\"]}","created_at":"2026-09-24T22:07:49"}]}