Question

Rationalise
3+2
3-2 ​

Answer 1

Question :

$\tt \purple{Rationalise \: the \: denominator : } \frac{ \sqrt{3} + 2 }{ \sqrt{3} - 2}$

Answer :

$\implies\tt{ \frac{ \sqrt{3} + 2 }{ \sqrt{3} - 2 } \times\frac{ \sqrt{3} + 2 }{ \sqrt{3} + 2} }$

$\tt \red{ Formula \: used : ({a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab}$

$\implies \tt{ \frac{ (\sqrt{3} + 2) {}^{2} }{3 - 2} }$

$\implies\tt{ \frac{ ( \sqrt{3} ) {}^{2} + ({2)}^{2} + 2 \times \sqrt{3} \times 2 }{1} }$

$\implies\tt{{3 + 4 + 4 \sqrt{3} }}$

$\implies\boxed{\tt{7 + 4 \sqrt{3} }} \orange \bigstar$