s the first step to simplify a surd like $\\sqrt{72}$?","back":"Find the largest perfect-square factor of the number.","points":1},{"id":"46fda38a-2d26-4ebd-95a1-331b9b4a508f","cardType":"basic","front":"Simplify $\\sqrt{72}$ into the form $k\\sqrt{2}$.","back":"$$\\sqrt{36 \\times 2} = 6\\sqrt{2}$","points":2},{"id":"b2e8bef0-dedf-4270-ab74-153f98b2fc01","cardType":"cloze","front":"While $\\sqrt{ab} = \\sqrt{a}\\sqrt{b}$ is true, the expression $\\sqrt{a+b}$ [ ] $\\sqrt{a}+\\sqrt{b}$.","back":"While $\\sqrt{ab} = \\sqrt{a}\\sqrt{b}$ is true, the expression $\\sqrt{a+b}$ is not equal to $\\sqrt{a}+\\sqrt{b}$.","points":null},{"id":"2108fbe4-2136-4e87-9d94-2568ef35b572","cardType":"basic","front":"What are like surds?","back":"Surds that have the same root part (e.g. $3\\sqrt{7}$ and $5\\sqrt{7}$).","points":1},{"id":"6469f1da-b796-4afb-a203-4d7224486837","cardType":"basic","front":"Simplify $12\\sqrt{3} + 10\\sqrt{3}$.","back":"$$22\\sqrt{3}$","points":1},{"id":"3ed523a1-5949-4749-95f5-5cc071247d8a","cardType":"basic","front":"How do you simplify a surd with a coefficient, such as $4\\sqrt{45}$?","back":"

Simplify the root: $\\sqrt{45} = 3\\sqrt{5}$
Multiply by the coefficient: $4 \\times 3\\sqrt{5} = 12\\sqrt{5}$

","points":2},{"id":"6dcdb9a0-c5d4-466f-91f4-47d678079216","cardType":"basic","front":"What is the result of $\\sqrt{a} \\times \\sqrt{a}$?","back":"$$a$","points":1},{"id":"f16db7ad-d212-426d-ae3a-c27133f0f799","cardType":"cloze","front":"Two expressions such as $a+\\sqrt{b}$ and $a-\\sqrt{b}$ are known as [ ].","back":"Two expressions such as $a+\\sqrt{b}$ and $a-\\sqrt{b}$ are known as conjugates.","points":null},{"id":"892534ad-0e8c-444f-93d9-6e5ef85309d2","cardType":"basic","front":"What is the simplified result of the product $(a+\\sqrt{b})(a-\\sqrt{b})$?","back":"$$a^2 - b$","points":2},{"id":"529523e8-b7b5-4a67-8d7b-da363f2a9db0","cardType":"basic","front":"When squaring a bracket like $(3-\\sqrt{5})^2$, why is it helpful to write it as two identical brackets?","back":"To ensure the middle terms are included in the expansion.","points":1},{"id":"4d8b48b5-7c24-4416-8186-1cb4e5f3b569","cardType":"basic","front":"Expand and simplify $(5+\\sqrt{6})(5-\\sqrt{6})$.","back":"$$25 - 6 = 19$","points":2},{"id":"b489744a-00eb-4e7f-982a-36eeeec37bac","cardType":"basic","front":"What is the objective of rationalising a denominator?","back":"To rewrite the fraction so there is no surd in the denominator.","points":1},{"id":"90dbe8ce-b99b-4c03-a4c4-0dfd62c96d2f","cardType":"basic","front":"How do you rationalise a fraction with a single surd denominator $\\frac{k}{\\sqrt{a}}$?","back":"Multiply both the numerator and denominator by $\\sqrt{a}$.","points":1},{"id":"a66b647e-3275-488c-a45c-8dca5ce693f1","cardType":"cloze","front":"To rationalise a denominator with two terms, such as $3+\\sqrt{2}$, you must multiply the numerator and denominator by the [ ].","back":"To rationalise a denominator with two terms, such as $3+\\sqrt{2}$, you must multiply the numerator and denominator by the conjugate.","points":null},{"id":"fb8cc97e-88ba-4713-8dcd-a3865f54f87c","cardType":"basic","front":"Simplify $\\frac{12}{\\sqrt{3}}$ fully.","back":"$$\\frac{12\\sqrt{3}}{3} = 4\\sqrt{3}$","points":2},{"id":"c5835a17-f75d-43bb-84c0-41219914d5de","cardType":"basic","front":"Simplify the algebraic surd expression $(\\sqrt{x}+\\sqrt{y})(\\sqrt{x}-\\sqrt{y})$.","back":"$$x - y$","points":2},{"id":"78646f5d-cece-476d-83e3-e5360a1fa023","cardType":"basic","front":"Expand and simplify $(3p+\\sqrt{q})^2$.","back":"$$9p^2 + 6p\\sqrt{q} + q$","points":2}]}],"examCountdown":{"examDate

Surds Flashcards

Surds Flashcards

Surds Flashcards

Surds Flashcards