1964","topicSlug":"surds","cards":[{"id":"8c95d735-95e8-4718-94ba-be6bd95114f5","cardType":"basic","front":"Why is $\\sqrt{10}$ a surd but $\\sqrt{16}$ is not?","back":"$$\\sqrt{10}$ is irrational, while $\\sqrt{16}=4$ is rational.","points":2,"mcqOptions":null},{"id":"516aba78-5c62-46ec-bcd8-764be298bc29","cardType":"basic","front":"Why should $\\sqrt{2}$ be used instead of $1.414$ for an exact answer?","back":"$$\\sqrt{2}$ is exact; $1.414$ is an approximation.","points":2,"mcqOptions":null},{"id":"22471c77-df8f-4d43-b273-f7c35e9a1fdf","cardType":"basic","front":"In $a^{\\frac{m}{n}}$, what does the denominator $n$ represent?","back":"The denominator gives the root.","points":1,"mcqOptions":null},{"id":"0987fdb8-02de-4538-abdb-17b040791d8f","cardType":"basic","front":"In $a^{\\frac{m}{n}}$, what does the numerator $m$ represent?","back":"The numerator gives the power.","points":1,"mcqOptions":null},{"id":"bfc29d5c-4191-407d-9a4c-6288eb94fa4a","cardType":"basic","front":"Write $x^{\\frac{3}{2}}$ in surd notation.","back":"$\\sqrt{x^3}$ or $(\\sqrt{x})^3$.","points":1,"mcqOptions":null},{"id":"eafae85f-7d12-4f8d-9124-cfd60adfb37b","cardType":"basic","front":"Write $\\sqrt[3]{y^2}$ in fractional-index notation.","back":"$y^{\\frac{2}{3}}$.","points":1,"mcqOptions":null},{"id":"4100af17-953f-4496-a97a-a93be9ddb083","cardType":"basic","front":"What restriction is required for $\\sqrt{a}$ to be real?","back":"$a\\geq 0$.","points":1,"mcqOptions":null},{"id":"473dee26-03bf-4018-9601-0ae7d7b2bd90","cardType":"cloze","front":"The root-index equivalences are $\\sqrt[n]{a}=$ $\\text{[...]}$ and $\\sqrt[n]{a^m}=$ $a^{\\frac{m}{n}}$.","back":"The root-index equivalences are $\\sqrt[n]{a}=$ $\\boxed{a^{\\frac{1}{n}}}$ and $\\sqrt[n]{a^m}=$ $a^{\\frac{m}{n}}$.","points":null,"mcqOptions":null},{"id":"278ecdbc-fe91-4d8b-b8ad-ab74016145b5","cardType":"cloze","front":"The root-index equivalences are $\\sqrt[n]{a}=$ $a^{\\frac{1}{n}}$ and $\\sqrt[n]{a^m}=$ $\\text{[...]}$.","back":"The root-index equivalences are $\\sqrt[n]{a}=$ $a^{\\frac{1}{n}}$ and $\\sqrt[n]{a^m}=$ $\\boxed{a^{\\frac{m}{n}}}$.","points":null,"mcqOptions":null},{"id":"25896e64-ea96-438a-993a-a46da9067e9b","cardType":"basic","front":"Why can a perfect-square factor be taken outside a square root?","back":"Because $\\sqrt{ab}=\\sqrt{a}\\sqrt{b}$ for non-negative $a,b$.","points":2,"mcqOptions":null},{"id":"deeff0e9-06c0-4443-a0d0-ed3bc496e6da","cardType":"basic","front":"Simplify $\\sqrt{72}$.","back":"$6\\sqrt{2}$.","points":1,"mcqOptions":null},{"id":"b5a0cdc9-9016-4c63-8386-76da5ae39437","cardType":"basic","front":"Why is $3\\sqrt{8}$ not fully simplified?","back":"Because $\\sqrt{8}=2\\sqrt{2}$, giving $6\\sqrt{2}$.","points":2,"mcqOptions":null},{"id":"4b83945e-2b5a-4254-a875-67a0d71b3544","cardType":"basic","front":"What is wrong with simplifying $\\sqrt{a+b}$ as $\\sqrt{a}+\\sqrt{b}$?","back":"The root product rule applies to products, not sums.","points":2,"mcqOptions":null},{"id":"681cec9a-3b09-40d9-8ea2-c1309fbaaf3b","cardType":"cloze","front":"Like surds combine according to $a\\sqrt{n}+b\\sqrt{n}=$ $\\text{[...]}$, while $(\\sqrt{a})^2=$ $a$ for $a\\geq0$.","back":"Like surds combine according to $a\\sqrt{n}+b\\sqrt{n}=$ $\\boxed{(a+b)\\sqrt{n}}$, while $(\\sqrt{a})^2=$ $a$ for $a\\geq0$.","points":null,"mcqOptions":null},{"id":"70f4088c-6d2d-4110-ad69-3b32a2694f76","cardType":"cloze","front":"Like surds combine according to $a\\sqrt{n}+b\\sqrt{n}=$ $(a+b)\\sqrt{n}$, while $(\\sqrt{a})^2=$ $\\text{[...]}$ for $a\\geq0$.","back":"Like surds combine according to $a\\sqrt{n}+b\\sqrt{n}=$ $(a+b)\\sqrt{n}$, while $(\\sqrt{a})^2=$ $\\boxed{a}$ for $a\\geq0$.","points":null,"mcqOptions":null},{"id":"a32f1013-41e9-4524-961d-8fc292dcdd4b","cardType":"basic","front":"Simplify $\\sqrt{12}+2\\sqrt{27}-\\sqrt{3}$.","back":"$7\\sqrt{3}$.","points":2,"mcqO

1.2.2 Surds Flashcards

1.2.2 Surds Flashcards