46f2","topicSlug":"surds","cards":[{"id":"d4226772-ee00-49bc-acb1-ce555690b2ad","cardType":"basic","front":"What value does $\\sqrt{25}$ denote, even though both 5 and -5 solve $x^2=25$?","back":"$$\\sqrt{25}=\\strong{5}$, the positive square root.","points":1,"mcqOptions":null},{"id":"b823e642-f563-42c4-a2b5-372d57009712","cardType":"cloze","front":"The symbol $\\sqrt{a}$ denotes the [ ] square root of $a$. Keeping an irrational root as a surd gives an exact value.","back":"The symbol $\\sqrt{a}$ denotes the positive square root of $a$. Keeping an irrational root as a surd gives an exact value.","points":null,"mcqOptions":null},{"id":"6cd13363-9021-42ba-ac28-86dd8da2863a","cardType":"cloze","front":"The symbol $\\sqrt{a}$ denotes the positive square root of $a$. Keeping an irrational root as a surd gives an [ ] value.","back":"The symbol $\\sqrt{a}$ denotes the positive square root of $a$. Keeping an irrational root as a surd gives an exact value.","points":null,"mcqOptions":null},{"id":"ba82bafa-f496-4046-a529-c64ed1a38210","cardType":"basic","front":"Why should $\\sqrt{3}$ be kept instead of replacing it with 1.732?","back":"$$\\sqrt{3}$ is exact; 1.732 contains rounding error.","points":2,"mcqOptions":null},{"id":"b8f50795-bac5-4f4a-a621-7c2b86c2c0ec","cardType":"cloze","front":"For $a,b\\geq0$, $\\sqrt{a}\\sqrt{b}=$ $\\text{[...]}$. For $b>0$, $\\dfrac{\\sqrt{a}}{\\sqrt{b}}=$ $\\sqrt{\\dfrac{a}{b}}$.","back":"For $a,b\\geq0$, $\\sqrt{a}\\sqrt{b}=$ $\\boxed{\\sqrt{ab}}$. For $b>0$, $\\dfrac{\\sqrt{a}}{\\sqrt{b}}=$ $\\sqrt{\\dfrac{a}{b}}$.","points":null,"mcqOptions":null},{"id":"e021a455-66cd-4ced-a60c-77b473dd9282","cardType":"cloze","front":"For $a,b\\geq0$, $\\sqrt{a}\\sqrt{b}=$ $\\sqrt{ab}$. For $b>0$, $\\dfrac{\\sqrt{a}}{\\sqrt{b}}=$ $\\text{[...]}$.","back":"For $a,b\\geq0$, $\\sqrt{a}\\sqrt{b}=$ $\\sqrt{ab}$. For $b>0$, $\\dfrac{\\sqrt{a}}{\\sqrt{b}}=$ $\\boxed{\\sqrt{\\dfrac{a}{b}}}$.","points":null,"mcqOptions":null},{"id":"cbed5b5d-367e-4705-a986-34fec6c70583","cardType":"basic","front":"Can $\\sqrt{a+b}$ generally be rewritten as $\\sqrt{a}+\\sqrt{b}$?","back":"No; square roots do not distribute over addition.","points":1,"mcqOptions":null},{"id":"85b0f95f-3c8a-4f6d-82b6-20ddff157d6f","cardType":"basic","front":"Simplify $\\sqrt{72}$.","back":"$6\\sqrt{2}$","points":2,"mcqOptions":null},{"id":"206c81c2-347c-48da-910c-bc53e2c62df6","cardType":"basic","front":"Simplify $\\sqrt{6}\\times\\sqrt{15}$.","back":"$3\\sqrt{10}$","points":2,"mcqOptions":null},{"id":"ab8ff5b2-1376-4cf7-b43c-9127f555501e","cardType":"basic","front":"Simplify $\\sqrt{48}+2\\sqrt{27}-\\sqrt{3}$.","back":"$9\\sqrt{3}$","points":2,"mcqOptions":null},{"id":"0b675d05-ed96-44f4-ad5b-afe084de6b83","cardType":"basic","front":"Expand and simplify $(3+\\sqrt{5})(2-\\sqrt{5})$.","back":"$1-\\sqrt{5}$","points":2,"mcqOptions":null},{"id":"f2d4c4d0-6cf8-4e09-857c-05a5f029805c","cardType":"cloze","front":"The conjugate of $a+\\sqrt{b}$ is $\\text{[...]}$, and $(a+\\sqrt{b})(a-\\sqrt{b})=$ $a^2-b$.","back":"The conjugate of $a+\\sqrt{b}$ is $\\boxed{a-\\sqrt{b}}$, and $(a+\\sqrt{b})(a-\\sqrt{b})=$ $a^2-b$.","points":null,"mcqOptions":null},{"id":"857c1086-4e48-4e27-a527-d200dc7fe9f9","cardType":"cloze","front":"The conjugate of $a+\\sqrt{b}$ is $a-\\sqrt{b}$, and $(a+\\sqrt{b})(a-\\sqrt{b})=$ $\\text{[...]}$.","back":"The conjugate of $a+\\sqrt{b}$ is $a-\\sqrt{b}$, and $(a+\\sqrt{b})(a-\\sqrt{b})=$ $\\boxed{a^2-b}$.","points":null,"mcqOptions":null},{"id":"0d1d9f08-33a3-4d8a-bddf-d0a85b133680","cardType":"basic","front":"What is the conjugate of $3-\\sqrt{2}$?","back":"$3+\\sqrt{2}$","points":1,"mcqOptions":null},{"id":"1bb9c257-e112-4326-bf5c-a09d0ef435a0","cardType":"basic","front":"Simplify $(4+\\sqrt{

1.5.2 Surds Flashcards

1.5.2 Surds Flashcards