// Numbas version: exam_results_page_options {"name": "Inbbavathie's copy of Surds simplification", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"parts": [{"type": "m_n_x", "variableReplacements": [], "prompt": "
For the following examples, tick the correct box to determine whether or not they are a surd.
\n", "scripts": {}, "variableReplacementStrategy": "originalfirst", "choices": ["$\\sqrt{\\var{square}}$
", "$\\sqrt{\\var{h}}$
", "$^3\\sqrt{\\var{cube}}$
", "$\\sqrt{\\var{j}}$
", "$\\sqrt{\\var{k}}$
"], "maxAnswers": 0, "maxMarks": 0, "showCorrectAnswer": true, "shuffleChoices": false, "matrix": [[0, "1"], ["1", 0], [0, "1"], ["1", "0"], ["1", 0]], "shuffleAnswers": false, "answers": ["Surd
", "Not a surd
"], "marks": 0, "warningType": "none", "minMarks": 0, "displayType": "radiogroup", "showFeedbackIcon": true, "minAnswers": 0, "layout": {"type": "all", "expression": ""}}, {"type": "gapfill", "variableReplacements": [], "prompt": "Match each surd with the equivalent simplification.
\n[[0]]
", "scripts": {}, "marks": 0, "showFeedbackIcon": true, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "gaps": [{"type": "m_n_x", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "minMarks": 0, "choices": ["i) $\\sqrt{48}$
", "ii) $\\sqrt{32}$
", "iii) $\\sqrt{56}$
", "iv) $\\sqrt{44}$
"], "maxAnswers": 0, "maxMarks": 0, "showCorrectAnswer": true, "shuffleChoices": true, "matrix": [["1", 0, 0, "0"], [0, "0", "0", "1"], ["0", "0", "1", 0], [0, "1", 0, 0]], "shuffleAnswers": true, "answers": ["$4\\sqrt3$
", "$2\\sqrt{11}$
", "$2\\sqrt{14}$
", "$4\\sqrt{2}$
"], "marks": 0, "warningType": "none", "scripts": {}, "displayType": "radiogroup", "showFeedbackIcon": true, "minAnswers": 0, "layout": {"type": "all", "expression": ""}}]}, {"type": "gapfill", "variableReplacements": [], "prompt": "Simplify the following surds:
\n$\\displaystyle\\sqrt{\\var{c}}$ = [[0]]$\\displaystyle\\sqrt{\\var{b}}$
\n$\\displaystyle\\sqrt{\\var{g}}$ = [[1]]$\\displaystyle\\sqrt{\\var{f}}$
\n", "scripts": {}, "marks": 0, "showFeedbackIcon": true, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "gaps": [{"correctAnswerFraction": false, "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "mustBeReduced": false, "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "minValue": "sqrta", "type": "numberentry", "allowFractions": false, "marks": 1, "notationStyles": ["plain", "en", "si-en"], "maxValue": "sqrta"}, {"correctAnswerFraction": false, "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "mustBeReduced": false, "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "minValue": "sqrtd", "type": "numberentry", "allowFractions": false, "marks": 1, "notationStyles": ["plain", "en", "si-en"], "maxValue": "sqrtd"}]}], "variablesTest": {"maxRuns": 100, "condition": ""}, "variable_groups": [], "statement": "Surds are square roots that cannot be simplified to a whole number. They have a decimal equivalent but their decimal representations are never-ending. Therefore, it is often easier to leave surds as they are in algebraic calculations.
", "variables": {"cube": {"name": "cube", "definition": "Random(8,27,64,125)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "sqrtd": {"name": "sqrtd", "definition": "sqrt(d)", "templateType": "anything", "group": "Ungrouped variables", "description": "square root of the selected square number d.
"}, "c": {"name": "c", "definition": "a*b", "templateType": "anything", "group": "Ungrouped variables", "description": "a times b
"}, "g": {"name": "g", "definition": "d*f", "templateType": "anything", "group": "Ungrouped variables", "description": "d times f
"}, "j": {"name": "j", "definition": "random(1..10 except 4 except 9 except h except 1)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "d": {"name": "d", "definition": "random(doptions except a)", "templateType": "anything", "group": "Ungrouped variables", "description": "Random squared number but not the same number as a.
"}, "f": {"name": "f", "definition": "random(2..12 except 4 except 9)", "templateType": "anything", "group": "Ungrouped variables", "description": "Random number between 2 and 12
"}, "a": {"name": "a", "definition": "random(aoptions)", "templateType": "anything", "group": "Ungrouped variables", "description": "Random squared number
"}, "doptions": {"name": "doptions", "definition": "[ 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 ]", "templateType": "list of numbers", "group": "Ungrouped variables", "description": "List of squared numbers from 1 to 144
"}, "h": {"name": "h", "definition": "random(1..10 except 4 except 9 except 1)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "aoptions": {"name": "aoptions", "definition": "[ 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 ]", "templateType": "list of numbers", "group": "Ungrouped variables", "description": "List of random square number between 1 and 36
"}, "sqrta": {"name": "sqrta", "definition": "sqrt(a)", "templateType": "anything", "group": "Ungrouped variables", "description": "square root of the squared numbers
"}, "root": {"name": "root", "definition": "root(cube,3)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "b": {"name": "b", "definition": "random(2..12 except 4 except 9)", "templateType": "anything", "group": "Ungrouped variables", "description": "Random number between 1 and 12 except 4 and 9.
"}, "k": {"name": "k", "definition": "random(10..15 except h except j)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "square": {"name": "square", "definition": "Random(4,9,16,25,36,49,64,81,100)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}}, "name": "Inbbavathie's copy of Surds simplification", "extensions": [], "ungrouped_variables": ["aoptions", "b", "a", "c", "sqrta", "doptions", "sqrtd", "d", "f", "g", "square", "cube", "h", "j", "k", "root"], "tags": ["not a surd", "simplification of surds", "simplifying surds", "surds"], "advice": "$\\sqrt{\\var{square}}$ and $\\sqrt[3]{\\var{cube}}$ are not surds, as they can be simplified to whole integers: $\\simplify{{sqrt(square)}}$ and $\\var{root}$ respectively. They are roots, but not surds. All surds are roots but not all roots are surds.
\n$\\sqrt{\\var{h}}$, $\\sqrt{\\var{j}}$ and $\\sqrt{\\var{k}}$ are surds, as they cannot be simplified to a whole integer. There is no number, $b$, such that $b^2=\\var{h}, \\var{j}$ or $\\var{k}$. Therefore, $\\sqrt{\\var{h}}$, $\\sqrt{\\var{j}}$ and $\\sqrt{\\var{k}}$ are both roots and surds.
\n\n\nThe rule that should be used is $\\sqrt{a}\\times\\sqrt{b}=\\sqrt{ab}$.
\nWe need to try to find a square number that divides $ab$ and rewrite this as $\\sqrt{b^2}\\times\\sqrt{a}$.
\ni)
\n$\\sqrt{48}$ = $\\sqrt{16}\\times\\sqrt3$
\n$\\sqrt{16}$ simplifies down to $4$ so the final answer is: $4\\sqrt3$.
\nii)
\n$\\sqrt{56}$ = $\\sqrt{4}\\times\\sqrt{14}$
\n$\\sqrt4$ simplifies down to $2$ so the final answer is: $2\\sqrt{14}$.
\niii)
\n$\\sqrt{32}$ = $\\sqrt{16}\\times\\sqrt{2}$
\n$\\sqrt{16}$ simplifies down to $4$ so the final answer is: $4\\sqrt2$.
\niv)
\n$\\sqrt{44}$ = $\\sqrt{4}\\times\\sqrt{11}$
\n$\\sqrt4$ simplifies down to $2$ so the final answer is: $2\\sqrt{11}$.
\n\nThis question requires you to notice that $\\sqrt{\\var{a}}$ and $\\sqrt{\\var{d}}$ are squared numbers and can be simplified to integers.
\n$\\sqrt{\\var{a}}$ = $\\var{sqrta}$ such that:
\ni) $\\sqrt{\\var{c}}$ = $\\sqrt{\\var{a}}$ x $\\sqrt{\\var{b}}$ = $\\var{sqrta}\\sqrt{\\var{b}}$ and
\nii) $\\sqrt{\\var{g}}$ = $\\sqrt{\\var{d}}$ x $\\sqrt{\\var{f}}$ = $\\var{sqrtd}\\sqrt{\\var{f}}$.
\n\n", "preamble": {"css": "", "js": ""}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "This question tests the student's understanding of what is and is not a surd, and on their simplification of surds.
"}, "functions": {}, "rulesets": {}, "type": "question", "contributors": [{"name": "Inbbavathie Ravi", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1620/"}]}]}], "contributors": [{"name": "Inbbavathie Ravi", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1620/"}]}