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{"name": "00b - Engineering Arithmetic: 002", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "advice": "<p>a)&nbsp; &nbsp;Since&nbsp; $\\var{a1} \\times \\var{a1}=\\var{a2}$&nbsp; and also $(-\\var{a1}) \\times (-\\var{a1})=\\var{a2}$,&nbsp; so:</p>\n<p>\\[\\pm \\sqrt{\\var{a2}}=\\pm \\var{a1}\\]</p>\n<p>b)&nbsp; &nbsp;Using your calculator:</p>\n<p>\\[\\pm \\sqrt{\\var{b2}}=\\pm \\var{b1}\\]</p>\n<p>c)&nbsp; &nbsp;Similarly:</p>\n<p>\\[ \\sqrt{\\var{c2}}=\\var{c1}\\]</p>\n<p>d)&nbsp; &nbsp;Your calculator will have a&nbsp; $\\sqrt[3]{}$&nbsp; button. Use it to evaluate:</p>\n<p>\\[ \\sqrt[3]{\\var{d2}}=\\var{d1}\\]</p>\n<p>e)&nbsp; &nbsp;</p>\n<p>\\[ \\sqrt[3]{\\var{e2}}=\\var{e1}\\]</p>\n<p>f)&nbsp; &nbsp;Since we need the 4<sup>th</sup> root (even) of $\\var{f2}$, we will have two numbers. Using your calculator:</p>\n<p>\\[\\pm \\sqrt[4]{\\var{f2}}=\\pm \\var{f1}\\]</p>\n<p>g)&nbsp; &nbsp;</p>\n<p>\\[\\pm \\sqrt[4]{\\var{g2}}=\\pm \\var{g1}\\]</p>\n<p>h)&nbsp; &nbsp;Again, the calculator shows the 8<sup>th</sup> root (even) of $\\var{h2}$ as&nbsp; $\\var{h1}$. Are there any other roots? Yes,&nbsp;$-\\var{h1}$. Hence:</p>\n<p>\\[\\pm \\sqrt[8]{\\var{h2}}=\\pm \\var{h1}\\]</p>\n<p>i)&nbsp; &nbsp;Using the calculator gives&nbsp; &nbsp;$ \\sqrt[5]{\\var{i2}}=\\var{i1}$</p>\n<p>j)&nbsp; &nbsp;Since we are interested in the 5<sup>th</sup> root (odd), there can only be one answer:</p>\n<p>\\[ \\sqrt[5]{(\\var{j2})}=\\var{j1}\\]</p>", "extensions": [], "statement": "<p>Using your calculator or otherwise, compute:</p>", "tags": [], "rulesets": {}, "ungrouped_variables": ["a1", "a2", "b1", "b2", "c1", "c2", "d1", "d2", "e1", "e2", "f1", "f2", "g1", "g2", "h1", "h2", "i1", "i2", "j1", "j2"], "variable_groups": [], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Indices and Roots</p><p>Questions based on Exercise Intro(b) from the Textbook \"Engineering Maths through Applications\" by Kuldeep Singh.</p><p>Intended for use as Homework Exercises.</p>"}, "name": "00b - Engineering Arithmetic: 002", "variablesTest": {"condition": "", "maxRuns": 100}, "parts": 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