Question

Rationalise the question

Answer 1

let's recall that multiplying "a + b" by its conjugate "a - b" will give us a difference of squares, so to rationalize the denominator, let's multiply the fraction top and bottom by the conjugate of the denominator.

`\textit{difference of squares} \\\\ (a-b)(a+b) = a^2-b^2 \\\\[-0.35em] ~\dotfill`

`\cfrac{1}{√(3)+√(2)}\implies \stackrel{ \textit{rationalizing the denominator} }{\cfrac{1}{√(3)+√(2)}\cdot \cfrac{√(3)-√(2)}{√(3)-√(2)}\implies \cfrac{√(3)-√(2)}{\underset{ \textit{difference of squares} }{(√(3)+√(2))(√(3)-√(2))}}} \\\\\\ \cfrac{√(3)-√(2)}{(√(3))^2-(√(2))^2}\implies \cfrac{√(3)-√(2)}{3-2}\implies \cfrac{√(3)-√(2)}{1}\implies √(3)-√(2)`