Question

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Answer 1

Answer:

Given,

$\frac{3 \sqrt{5} + 2 \sqrt{3} }{3 \sqrt{5} - 2 \sqrt{3} }$

$\: \: \: = \frac{3 \sqrt{5} + 2 \sqrt{3} }{3 \sqrt{5} - 2 \sqrt{3} } \times \frac{3 \sqrt{5 } + 2 \sqrt{3} }{3 \sqrt{5} + 2 \sqrt{3} }$

$\: \: \: = \frac{(3 \sqrt{5} + 2 \sqrt{3} ) {}^{2} }{(3 \sqrt{5 }) {}^{2} - (2 \sqrt{3} ) {}^{2} }$

$\: \: \: = \frac{(3 \sqrt{5}) {}^{2} + 2(3 \sqrt{5})(2 \sqrt{3} ) + (2 \sqrt{3} ) {}^{2} }{9(5) - 4(3)}$

$\: \: \: = \frac{9(5) + 12\sqrt{15}+ 4(3)}{45 - 12}$

$\: \: \: = \frac{45 + 12\sqrt{15}+ 12}{33}$

$\: \: \: = \frac{57+ 12\sqrt{15}}{33}$

$\: \: \: = \frac{3(19 + 4\sqrt{15})}{33}$

$\: \: \: = \frac{19 + 4\sqrt{15}}{11}$

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Answer 2

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