// Numbas version: finer_feedback_settings
{"name": "Surds: simplifying", "extensions": [], "custom_part_types": [], "resources": [["question-resources/sqrt_Irff7Ni.png", "sqrt_Irff7Ni.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Surds: simplifying", "tags": ["irrationals", "surds", "Surds"], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"hardermult": {"name": "hardermult", "group": "Ungrouped variables", "definition": "hardersquareinfo[0][0]*hardersquareinfo[1][0]", "description": "", "templateType": "anything", "can_override": false}, "leftovers": {"name": "leftovers", "group": "Ungrouped variables", "definition": "listleftovers[0]*listleftovers[1]", "description": "", "templateType": "anything", "can_override": false}, "k": {"name": "k", "group": "Unnamed group", "definition": "random(1..6)", "description": "", "templateType": "anything", "can_override": false}, "easyprime": {"name": "easyprime", "group": "Ungrouped variables", "definition": "random(listprimes[0..5])", "description": "", "templateType": "anything", "can_override": false}, "hardersquareinfo": {"name": "hardersquareinfo", "group": "Unnamed group", "definition": "[random(listprimesquares[0..k]),random(listprimesquares[k..7])]", "description": "", "templateType": "anything", "can_override": false}, "listprimesquares": {"name": "listprimesquares", "group": "Unnamed group", "definition": "map([n,n^2],n,[2,3,5,7,11,13,17])", "description": "", "templateType": "anything", "can_override": false}, "listleftovers": {"name": "listleftovers", "group": "Ungrouped variables", "definition": "shuffle(listprimes)[0..2]", "description": "", "templateType": "anything", "can_override": false}, "easyargument": {"name": "easyargument", "group": "Ungrouped variables", "definition": "easysquareinfo[1]*easyprime", "description": "", "templateType": "anything", "can_override": false}, "easysquareinfo": {"name": "easysquareinfo", "group": "Ungrouped variables", "definition": "random(listsquares[0..11])", "description": "", "templateType": "anything", "can_override": false}, "listprimes": {"name": "listprimes", "group": "Ungrouped variables", "definition": "[2,3,5,7,11,13,17]", "description": "", "templateType": "anything", "can_override": false}, "harderargument": {"name": "harderargument", "group": "Ungrouped variables", "definition": "leftovers*hardersquareinfo[0][1]*hardersquareinfo[1][1]", "description": "", "templateType": "anything", "can_override": false}, "stillunder": {"name": "stillunder", "group": "Ungrouped variables", "definition": "leftovers*hardersquareinfo[1][1]", "description": "", "templateType": "anything", "can_override": false}, "listsquares": {"name": "listsquares", "group": "Ungrouped variables", "definition": "map([n,n^2],n,2..15)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["listsquares", "listprimes", "easysquareinfo", "easyprime", "easyargument", "listleftovers", "leftovers", "harderargument", "hardermult", "stillunder"], "variable_groups": [{"name": "Unnamed group", "variables": ["listprimesquares", "k", "hardersquareinfo"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Simplify the surd $\\sqrt{\\var{easyargument}}$, entering your numbers in the gaps provided.</p>\n<p></p>\n<table cellpadding=\"0\" style=\"text-align: right;\">\n<tbody>\n<tr>\n<td>[[0]]</td>\n<td style=\"background-image: url('resources/question-resources/sqrt_Irff7Ni.png'); background-repeat: no-repeat;\">&nbsp; &nbsp;$\\,\\,\\,\\,$[[1]]</td>\n</tr>\n</tbody>\n</table>", "stepsPenalty": "2", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The idea is to find a factor which is a square number, e.g. 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, ... We can then take the square root of that factor out the front of the square root, we can do this until the number left under the square root has no square factor.</p>\n<p>A key fact&nbsp;we use here&nbsp;is that $\\sqrt{a\\times b}=\\sqrt{a}\\times\\sqrt{b}$ &nbsp;for non-negative real numbers $a,b$.</p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$\\sqrt{\\var{easyargument}}$</td>\n<td style=\"text-align: center;\">$=$</td>\n<td style=\"text-align: left;\">$\\sqrt{\\var{easysquareinfo[1]}\\times\\var{easyprime}}$</td>\n<td style=\"text-align: left;\">(you find that $\\var{easysquareinfo[1]}$ is a square factor of $\\var{easyargument}$)</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td style=\"text-align: center;\">$=$</td>\n<td style=\"text-align: left;\">$\\sqrt{\\var{easysquareinfo[1]}}\\times\\sqrt{\\var{easyprime}}$</td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td style=\"text-align: center;\">$=$</td>\n<td style=\"text-align: left;\">$\\var{easysquareinfo[0]}\\times\\sqrt{\\var{easyprime}}$</td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td style=\"text-align: center;\">$=$</td>\n<td style=\"text-align: left;\">$\\var{easysquareinfo[0]}\\sqrt{\\var{easyprime}}$</td>\n<td style=\"text-align: left;\"></td>\n</tr>\n</tbody>\n</table>"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "easysquareinfo[0]", "maxValue": "easysquareinfo[0]", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "easyprime", "maxValue": "easyprime", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Simplify the surd $\\sqrt{\\var{harderargument}}$, entering your numbers in the gaps provided.</p>\n<p>For this question, we suggest you use a calculator to check for square factors of $\\var{harderargument}$. That is, check if a square factor ($2^2=4$, $3^2=9$, $5^2=25$, $7^2=49$ etc...) divides $\\var{harderargument}$ without a remainder. If one does, then proceed with the surd simplification as usual and then repeat by checking the new surd for square factors until there are no square factors in the surd.</p>\n<table cellpadding=\"0\" style=\"text-align: right;\">\n<tbody>\n<tr>\n<td>[[0]]</td>\n<td style=\"background-image: url('resources/question-resources/sqrt_Irff7Ni.png'); background-repeat: no-repeat;\">&nbsp; &nbsp;$\\,\\,\\,\\,$[[1]]</td>\n</tr>\n</tbody>\n</table>", "stepsPenalty": "2", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>This question is similar to the last one but has larger numbers so it is harder to spot the square factors.&nbsp;Because of this, a calculator, factor trees, divisibility tests and/or long division may be useful.</p>\n<p>The idea is to find all the factors of $\\var{harderargument}$ which are&nbsp;squares, e.g. 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, ...&nbsp;We can then take the square root of those factors out the front of the square root, we can do this until the number left under the square root has no square factors left.</p>\n<p></p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$\\sqrt{\\var{harderargument}}$</td>\n<td style=\"text-align: center;\">$=$</td>\n<td style=\"text-align: left;\">$\\sqrt{\\var{hardersquareinfo[0][1]}\\times\\var{stillunder}}$</td>\n<td style=\"text-align: left;\">(you might find that $\\var{hardersquareinfo[0][1]}$ is a square factor of $\\var{harderargument}$)</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td style=\"text-align: center;\">$=$</td>\n<td style=\"text-align: left;\">$\\sqrt{\\var{hardersquareinfo[0][1]}}\\times\\sqrt{\\var{stillunder}}$</td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td style=\"text-align: center;\">$=$</td>\n<td style=\"text-align: left;\">$\\var{hardersquareinfo[0][0]}\\sqrt{\\var{stillunder}}$</td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td style=\"text-align: center;\">$=$</td>\n<td style=\"text-align: left;\">$\\var{hardersquareinfo[0][0]}\\times\\sqrt{\\var{hardersquareinfo[1][1]}\\times\\var{leftovers}}$</td>\n<td style=\"text-align: left;\">(you might find that $\\var{hardersquareinfo[1][1]}$ is a square factor of $\\var{stillunder}$)</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td style=\"text-align: center;\">$=$</td>\n<td style=\"text-align: left;\">$\\var{hardersquareinfo[0][0]}\\times\\sqrt{\\var{hardersquareinfo[1][1]}}\\times\\sqrt{\\var{leftovers}}$</td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td style=\"text-align: center;\">$=$</td>\n<td style=\"text-align: left;\">$\\var{hardersquareinfo[0][0]}\\times\\var{hardersquareinfo[1][0]}\\times\\sqrt{\\var{leftovers}}$</td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td style=\"text-align: center;\">$=$</td>\n<td style=\"text-align: left;\">$\\var{hardermult}\\sqrt{\\var{leftovers}}$</td>\n<td style=\"text-align: left;\">(there are no square factors of $\\var{leftovers}$ so we are finished)</td>\n</tr>\n</tbody>\n</table>\n<p>&nbsp;</p>"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, 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