Question

#BeBrainlyContest
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2nd question....
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Rationalize the denominator of the following...


$\sqrt{2} \: + \: 3 \sqrt{5} \: \: \: \: \div \: \: \: \: \: 3 \sqrt{7} \: + \: 5 \sqrt{3}$

Answer 1

$<b><u><i>$ Rationalizing the denominator :

$= > \frac{ \sqrt{2} + 3 \sqrt{5} }{3 \sqrt{7} + 5 \sqrt{3} } \\ \\ = > \frac{ \sqrt{2} + 3 \sqrt{5} }{3 \sqrt{7} + 5 \sqrt{3} } \times \frac{3 \sqrt{7} - 5 \sqrt{3} }{3 \sqrt{7} - 5 \sqrt{3} } \\ \\ = > \frac{( \sqrt{2} + 3 \sqrt{5})(3 \sqrt{7} - 5 \sqrt{3} ) }{ {(3 \sqrt{7} )}^{2} - {(5 \sqrt{3} )}^{2} } \\ \\ = > \frac{ \sqrt{2} (3 \sqrt{7} - 5 \sqrt{3}) + 3 \sqrt{5} (3 \sqrt{7} - 5 \sqrt{3}) }{63 - 75} \\ \\ = > \frac{3 \sqrt{14} - 5 \sqrt{6} + 9 \sqrt{35} - 15 \sqrt{15} }{ - 12} \\ \\ = > \frac{ - (3 \sqrt{14} - 5 \sqrt{6} + 9 \sqrt{35} - 15 \sqrt{15}) }{12} \\ \\ = > \dfrac{- 3 \sqrt{14} + 5 \sqrt{6} - 9 \sqrt{35} + 15 \sqrt{15}}{12}$

Rationalized!

Answer 2

$\large \tt AHOY!! \:$

given :- (√2 + 3√5)/(3√7 + 5√3)

= (√2 + 3√5)/(3√7 + 5√3) × (3√7 - 5√3)/(3√7 - 5√3)

= (√2 + 3√5)(3√7 - 5√3)/(3√7 + 5√3)(3√7 - 5√3)

= √2(3√7 - 5√3) + 3√5(3√7 - 5√3)/(3√7)² -(5√3)²

= (3√14 - 5√6 + 9√35 - 15√15)/(63 - 75)

= (3√14 - 5√6 + 9√35 - 15√15)/-12

= -(3√14 - 5√6 + 9√35 - 15√15)/12

= (-3√14 + 5√6 - 9√35 + 15√15)/12

$\large \tt HOPE \: THIS \: HELPS!!$