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

Rationalise the denominator of 1/(5 - sqrt(2)) giving your answer in its simplest form
198k views
1 vote
Rationalise the denominator of
1/(5 - sqrt(2))
giving your answer in its simplest form

User Jonathan Webb
by
9.2k points

1 Answer

4 votes


\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}

User Nick Howard
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