// Numbas version: exam_results_page_options
{"name": "Surds: Simplifying Expressions 1b", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Surds: Simplifying Expressions 1b", "tags": [], "metadata": {"description": "<p>Simplifying surds from $a\\sqrt{b^2c}$ to $ab\\sqrt{c}$, where $a$, $b$ and $c$ are positive integers.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Write&nbsp;the following number in its simplest form:</p>\n<p>\\[ \\var{a}\\sqrt{\\var{b^2*c}} \\]</p>", "advice": "<p>To simplify $\\var{a}\\sqrt{\\var{b^2*c}}$ we want to first write&nbsp;the square root term as the product of a square number and another integer:</p>\n<p>\\[ \\var{a}\\sqrt{\\var{b^2*c}} =\\var{a} \\sqrt{\\var{b^2} \\times \\var{c}}. \\]</p>\n<p>We can then apply the rule $\\sqrt{ab} = \\sqrt{a} \\sqrt{b}$, allowing us to write the number in its simplest form:</p>\n<p>\\[ \\begin{split} \\var{a}\\sqrt{\\var{b^2*c}} &amp;\\,= \\var{a}\\sqrt{\\var{b^2}} \\sqrt{\\var{c}} \\\\ &amp;\\,= \\var{a*b} \\sqrt{\\var{c}} \\end{split} \\]</p>\n<p></p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(2..7 except 4)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(2..8)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random([2,3,5,6,7] except b)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p><em>You can type sqrt(x) to get $\\sqrt{x}$.</em></p>", "answer": "{a*b}sqrt({c})", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "mustmatchpattern": {"pattern": "{a*b}sqrt({c})", "partialCredit": 0, "message": "", "nameToCompare": ""}, "valuegenerators": []}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}]}]}], "contributors": [{"name": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}]}