Question

Rationalize the denominator2/√3+√7

Answer 1

$\huge\bf{\underline{\underline{\red{Solution:-}}}}$

$\frac{2}{ \sqrt{3} + \sqrt{7} } \\ \\ rationalizing \: the \: denominator \: \\ \\ \sf\implies\: \frac{2}{ \sqrt{3} + \sqrt{7} } \times \frac{ \sqrt{3} - \sqrt{7} }{ \sqrt{3} - \sqrt{7} } \\ \\\sf\implies\: \frac{2( \sqrt{3} - \sqrt{7)} }{ {( \sqrt{3}) }^{2} - { (\sqrt{7}) }^{2} } \\ \\ \sf\implies\: \frac{2 (\sqrt{3} - \sqrt{7} )}{3 - 7} \\ \\ \sf\implies\:\frac{2( \sqrt{3} - \sqrt{7} ) }{ - 4} \\ \\ \sf\implies\: \frac{ \sqrt{3} - \sqrt{7} }{ - 2}$