Question

2 √5 / 7 - √3 rationalise

Answer 1

`\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}`

the question asks us to rationalise the given term ! thus , we'll just have to remove the √3 from th denominator anyhow !

let's start ~

`(2 √(5) )/(7 - √(3) ) \\ \\ \implies \: (2 √(5) )/(7 - √(3) ) \: * \: (7 + √(3) )/(7 + √(3) ) = \frac{14 √(5) + 2 √(15) }{(7) {}^(2) - ( \sqrt{3) {}^(2) } } \\ \\ \implies (14 √(5) + 2 √(15) )/(49 - 3) \\ \\ \implies (14 √(5) + 2 √(15) )/(46) \\ \\ \implies \: \frac{\cancel{2}(7 \sqrt{5{} } \: + √(15) )}{\cancel{46} } \\ \\\bold\red{ \implies \: (7 √(5) + √(15) )/(23)}`

hope helpful :D