Question

Rationalise the denominator of
1/(5 - sqrt(2))
giving your answer in its simplest form

Answer 1

`\cfrac{1}{5-√(2)}\cdot \cfrac{5+√(2)}{5+√(2)}\implies \cfrac{5+√(2)}{\underset{ \textit{difference of squares} }{(5-√(2))(5+√(2))}}\implies \cfrac{5+√(2)}{(5)^2~~ - ~~(√(2))^2} \\\\\\ \cfrac{5+√(2)}{25-2}\implies \cfrac{5+√(2)}{23}`