{"id":"act_quizme:math:q3:04","source_id":"act_quizme","source_item_id":"math-q3-04","external_id":"ed41f3cec63a7fef","program":"ACT","section":"math","category_code":null,"category":null,"subcategory_code":null,"subcategory":null,"form_id":null,"passage_id":null,"position":4,"scored":true,"layout_warning":null,"stem":"Given i= the square root of negative 1 i = - 1 , what is the square root of 9 end root + the square root of negative 16 9 + - 16 ?","stimulus":"","stimulus_html":null,"stem_html":"<div class=\"math-question-wrap\"><div class=\"item-content\" id=\"p40\"> \t\t\t\t\t \t\t\t\t\t<p>Given <span style=\"white-space: nowrap;\"><span class=\"visually-hidden\">i= the square root of negative 1</span><math class=\"srTransform\"><mi>i</mi><mo>=</mo><msqrt><mo>-</mo><mn>1</mn></msqrt></math>,</span> what is <span style=\"white-space: nowrap;\"><span class=\"visually-hidden\">the square root of 9 end root + the square root of negative 16</span><math class=\"srTransform\"><msqrt><mn>9</mn></msqrt><mo>+</mo><msqrt><mo>-</mo><mn>16</mn></msqrt></math>?</span></p>  \t\t\t\t</div> \t\t\t\t</div>\n<div><div class=\"math-answer-select-wrap\"></div></div>","rationale_html":"<p><strong>F.</strong> <strong>Incorrect.</strong> Remember that you can only combine like terms. Try simplifying each radical individually and then only combining like terms.</p><p><strong>G.</strong> <strong>Incorrect.</strong> Remember that, in general, <span style=\"white-space: nowrap;\"><math><msqrt><mi>a</mi></msqrt><mo>+</mo><msqrt><mi>b</mi></msqrt><mo>≠</mo><msqrt><mi>a</mi><mo>+</mo><mi>b</mi></msqrt></math>.</span> Try simplifying each radical individually instead.</p><p><strong>H.</strong> <strong>Incorrect. </strong>You may have thought that <span style=\"white-space: nowrap;\"><math><msqrt><mo>-</mo><mn>1</mn></msqrt><mo>=</mo><mo>-</mo><mi>i</mi></math>.</span> Remember that <span style=\"white-space: nowrap;\"><math><msqrt><mo>-</mo><mn>1</mn></msqrt><mo>=</mo><mi>i</mi></math>.</span></p><p><strong>J.</strong> <strong>Correct.</strong> Take the square root of each term, and use&nbsp;<math><msqrt><mo>-</mo><mn>1</mn></msqrt><mo>=</mo><mi>i</mi></math>&nbsp;to simplify: <span style=\"white-space: nowrap;\"><math><msqrt><mn>9</mn></msqrt><mo>+</mo><msqrt><mo>-</mo><mn>16</mn></msqrt><mo>=</mo><msqrt><mn>9</mn></msqrt><mo>+</mo><msqrt><mn>16</mn></msqrt><msqrt><mo>-</mo><mn>1</mn></msqrt><mo>=</mo><mn>3</mn><mo>+</mo><mn>4</mn><mi>i</mi></math>.</span></p>","correct_answer":["J"],"equiv_key":"3119459003d145e0ef3a1287","has_media":false,"has_mathml":true,"has_table":false,"section_label":"Mathematics","options":[{"label":"F","content_html":"<p>7i</p>","ord":0},{"label":"G","content_html":"<p><span>i the square root of 7</span>i7</p>","ord":1},{"label":"H","content_html":"<p><span>3 minus 4i</span>3-4i</p>","ord":2},{"label":"J","content_html":"<p>3+4i</p>","ord":3}],"passage":null,"attribution":{"source_id":"act_quizme","source_name":"ACT QuizMe official practice questions","rights_holder":"ACT Education Corp.","canonical_url":"https://quizme.act.org/","retrieved_from":"https://quizme.act.org/","attribution":"Official ACT practice questions © ACT Education Corp., from the QuizMe practice quizzes at quizme.act.org.","disclaimer":"ACT® is a registered trademark of ACT Education Corp., which is not affiliated with, does not sponsor, and does not endorse this project.","license":"ACT Education Corp. copyright. Published free on the public web; not licensed for redistribution.","redistributable":false,"item_count":78},"equivalents":[]}