Question

Rationalise the denominator of


$\frac{1}{3 + \sqrt{2} }$
​

Answer 1

$\huge{\fcolorbox{yellow}{red}{\large{\fcolorbox{blue}{pink}{{\fcolorbox{orange}{aqua}{ \pink{✨ANSWER✨}}}}}}}$

$\frac{1}{3 + \sqrt{2} } \\ \\ \implies \frac{1 \times( 3 - \sqrt{2} )}{(3 + \sqrt{2} )\times (3 - \sqrt{2}) } \\ \\ \implies \frac{3 - \sqrt{2} }{ {(3)}^{2} - {( \sqrt{2} )}^{2} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \frac{3 - \sqrt{2} }{9 - 2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \boxed{\frac{3 - \sqrt{2} }{7} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Answer 2

ABCDEFGHIJKLMNOPQRSTUVWXYZ