Question

rationalise the denominator​

Answer 1

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Answer 2

$\sf \green{Question : } \: \sf \red{ \frac{ \sqrt{7} + \sqrt{3} }{ \sqrt{7} - \sqrt{2} } }$

$\sf \green{Solution : }$

$\sf{ \twoheadrightarrow \frac{\sqrt{7} + \sqrt{3}}{ \sqrt{7} - \sqrt{2} } \times \frac{ \sqrt{7} + \sqrt{2} }{ \sqrt{7} + \sqrt{2} } }$

$\sf{ \twoheadrightarrow \frac{( \sqrt{7} + \sqrt{3} )( \sqrt{7} + \sqrt{2} ) }{ { (\sqrt{7} )}^{2} - { (\sqrt{2}) }^{2} } }$

${ \rm{ \blue{《{a}^{2} - {b}^{2} = (a - b)(a + b) 》}}}$

$\sf{ \twoheadrightarrow\frac{ \sqrt{7}( \sqrt{7} + \sqrt{2} ) + \sqrt{3}( \sqrt{7} + \sqrt{2} )}{7 - 2} }$

$\sf{ \twoheadrightarrow\frac{7 + \sqrt{7} \sqrt{2} + \sqrt{3} \sqrt{7} + \sqrt{3} \sqrt{2} }{5} }$

$\sf{{ \pink{\twoheadrightarrow \frac{7 + \sqrt{14} + \sqrt{21} + \sqrt{6} }{5} }}}$