// Numbas version: exam_results_page_options {"name": "Eirik's copy of Solve equations which include a single root (e.g. \\sqrt{x}=blah)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"preamble": {"css": "", "js": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "advice": "

a) Given $\\sqrt[\\var{intpower}]{x}=\\var{intrhs}$, we raise both sides to the power of $\\var{intpower}$ to get $x$ by itself.

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$\\sqrt[\\var{intpower}]{x}$$=$$\\var{intrhs}$ 
 
$\\left(\\sqrt[\\var{intpower}]{x}\\right)^{\\var{intpower}}$$=$$\\simplify[basic]{({intrhs})^{intpower}}$
 
$x$$=$$\\var{intsoln}$
\n

\n

b) Given $\\simplify{{bxcoeff}y^(1/{bpower})+{bb}}=\\var{bc}$, we can rearrange the equation to get $y^\\frac{1}{\\var{bpower}}$ by itself and then we can raise both sides to the power of $\\var{bpower}$ to get $y$ by itself.

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$\\simplify{{bxcoeff}y^(1/{bpower})+{bb}}$$=$$\\var{bc}$ 
 
$\\simplify{{bxcoeff}y^(1/{bpower})}$$=$$\\simplify[basic]{{bc}-{bb}}$
 
$\\simplify{{bxcoeff}y^(1/{bpower})}$$=$$\\simplify{{bc-bb}}$
$y^\\frac{1}{\\var{bpower}}$$=$$\\simplify[!basic]{{bc-bb}/{bxcoeff}}$
$y^\\frac{1}{\\var{bpower}}$$=$$\\simplify{{bc-bb}/{bxcoeff}}$
$\\left(y^\\frac{1}{\\var{bpower}}\\right)^{\\var{bpower}}$$=$$\\simplify[basic]{({(bc-bb)/bxcoeff})^{bpower}}$
$y$$=$$\\var{bsoln}$
\n

\n

c) Given $\\displaystyle{\\simplify{(root(z+{db},{dpower}))/{ddenom}}}=\\var{dc}$, we can rearrange the equation to get $\\simplify{(root(z+{db},{dpower}))}$ by itself, then we can raise both sides to the power of $\\var{dpower}$, and finally rearrange to get $z$ by itself.

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$\\displaystyle{\\simplify{(root(z+{db},{dpower}))/{ddenom}}}$$=$$\\var{dc}$ 
 
$\\displaystyle{\\simplify{(root(z+{db},{dpower}))}}$$=$$\\simplify[basic]{{dc}*{ddenom}}$
 
$\\displaystyle{\\simplify{(root(z+{db},{dpower}))}}$$=$$\\var{dc*ddenom}$
$\\left(\\sqrt[\\var{dpower}]{\\simplify{z+{db}}}\\right)^\\var{dpower}$$=$$\\simplify[basic]{({dc*ddenom})^{dpower}}$
$\\simplify{z+{db}}$$=$$\\simplify[basic]{-{abs(dc*ddenom)}^{dpower}}$  $\\simplify[basic]{({abs(dc*ddenom)})^{dpower}}$  $\\simplify[basic]{({(dc*ddenom)})^{dpower}}$  
$z$$=$$\\simplify[basic]{-{abs(dc*ddenom)}^{dpower}-{db}}$  $\\simplify[basic]{({abs(dc*ddenom)})^{dpower}-{db}}$  $\\simplify[basic]{({(dc*ddenom)})^{dpower}-{db}}$  
", "functions": {}, "variable_groups": [{"variables": ["intpower", "intrhs", "intsoln"], "name": "a"}, {"variables": ["bpower", "bnice", "bsoln", "bxcoeff", "bb", "bc"], "name": "b"}], "variables": {"bxcoeff": {"definition": "random(-3..3 except 0..1)", "templateType": "anything", "group": "b", "description": "", "name": "bxcoeff"}, "dc": {"definition": "random(-100..100 except -1..1)", "templateType": "anything", "group": "Ungrouped variables", "description": "", "name": "dc"}, "bsoln": {"definition": "bnice^bpower", "templateType": "anything", "group": "b", "description": "", "name": "bsoln"}, "bc": {"definition": "bnice*bxcoeff+bb", "templateType": "anything", "group": "b", "description": "", "name": "bc"}, "bb": {"definition": "random(1..100)", "templateType": "anything", "group": "b", "description": "", "name": "bb"}, "bnice": {"definition": "switch(bpower=3 or bpower=2, random(-10..10 except -1..1), bpower=5 or bpower =4, random(-4..4 except -1..1), bpower=7 or bpower=6, random(-3..3 except -1..1), 2)", "templateType": "anything", "group": "b", "description": "

((bc-bb)/bxcoeff)^(1/bpower)

", "name": "bnice"}, "db": {"definition": "random(-100..100 except -1..1)", "templateType": "anything", "group": "Ungrouped variables", "description": "", "name": "db"}, "bpower": {"definition": "random(2..9)", "templateType": "anything", "group": "b", "description": "", "name": "bpower"}, "intsoln": {"definition": "intrhs^intpower", "templateType": "anything", "group": "a", "description": "", "name": "intsoln"}, "intpower": {"definition": "random(2..9)", "templateType": "anything", "group": "a", "description": "", "name": "intpower"}, "intrhs": {"definition": "switch(intpower=3 or intpower=4, random(2..12), intpower=5 or intpower=6, random(2..5), intpower=7 or intpower=8, random(2..3), 2)\n", "templateType": "anything", "group": "a", "description": "

intsoln^intpower

", "name": "intrhs"}, "dpower": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "description": "", "name": "dpower"}, "ddenom": {"definition": "random(2..15)", "templateType": "anything", "group": "Ungrouped variables", "description": "", "name": "ddenom"}}, "parts": [{"gaps": [{"scripts": {}, "checkingtype": "absdiff", "vsetrange": [0, 1], "expectedvariablenames": [], "variableReplacements": [], "checkingaccuracy": 0.001, "showpreview": true, "marks": 1, "checkvariablenames": false, "type": "jme", "answer": "{intsoln}", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "vsetrangepoints": 5, "showFeedbackIcon": true}], "prompt": "

If  $\\sqrt[\\var{intpower}]{x}=\\var{intrhs}$, then $x=$ [[0]].

", "marks": 0, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "type": "gapfill", "scripts": {}}, {"gaps": [{"scripts": {}, "checkingtype": "absdiff", "vsetrange": [0, 1], "expectedvariablenames": [], "variableReplacements": [], "checkingaccuracy": 0.001, "showpreview": true, "marks": 1, "checkvariablenames": false, "type": "jme", "answer": "{bsoln}", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "vsetrangepoints": 5, "showFeedbackIcon": true}], "prompt": "

If  $\\simplify{{bxcoeff}y^(1/{bpower})+{bb}}=\\var{bc}$, then $y=$ [[0]].

", "marks": 0, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "type": "gapfill", "scripts": {}}, {"gaps": [{"scripts": {}, "checkingtype": "absdiff", "vsetrange": [0, 1], "expectedvariablenames": [], "variableReplacements": [], "checkingaccuracy": 0.001, "showpreview": true, "marks": 1, "answersimplification": "basic", "checkvariablenames": false, "type": "jme", "answer": "({dc*ddenom})^({dpower})-{db}", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "vsetrangepoints": 5, "showFeedbackIcon": true}], "prompt": "

For this question, if the answer was $\\left(\\frac{35}{11}\\right)^{11}-24$, then you could enter  (35/11)^(11)-24.

\n

If  $\\displaystyle{\\simplify{(root(z+{db},{dpower}))/{ddenom}}}=\\var{dc}$, then $z=$ [[0]].

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Questions to test if the student knows the inverse of fractional power or root (and how to solve equations that contain them). 

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "extensions": [], "statement": "

Please complete the following.

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