Question

Page : 1.7
Find the equivalent fraction with rational denominator of $\frac {8 \sqrt{3}-3 \sqrt{5} }{9 \sqrt{3} - 4 \sqrt {5}}$ :
$a) \: \: \frac {156 + 5 \sqrt{15} }{163} \\ b) \: \: \frac {15 + 3 \sqrt{15} }{16} \\ c) \: \: \frac {16 + 5 \sqrt{5} }{13} \\ d) \: \: \frac {6 + \sqrt{15} }{3}$

Answer 1

Heya!!

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Answer 2

The answer is
$given \\ \\ \frac {8 \sqrt{3}-3 \sqrt{5} }{9 \sqrt{3} - 4 \sqrt {5}} \\ \\ now \: \: we \: \: multiply \: \: the \: \: denominator \\ by \: \: the \: \: conjugate \: \: irrational \\ number \: (9 \sqrt{3} + 4 \sqrt{5} ) \\ \\ so \\ \frac {8 \sqrt{3}-3 \sqrt{5} }{9 \sqrt{3} - 4 \sqrt {5}} \times \frac {9 \sqrt{3} + 4 \sqrt{5} }{9 \sqrt{3} + 4 \sqrt {5}} \\ \\ = \frac{(8 \sqrt{3} - 3 \sqrt{5})(9 \sqrt{3} + 4 \sqrt{5} )}{( 9 \sqrt{3} - 4 \sqrt{5} )(9 \sqrt{3} + 4 \sqrt{5} ) } \\ \\ = \frac{216 + 32 \sqrt{15} - 27 \sqrt{15} - 60}{243 - 80} \\ \\ = \frac{156 + 5 \sqrt{15} }{163} \\ \\ therefore \: \: the \: \: first \: \: option \\ is \: \: correct$

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