Question

Rationalize the denominator of :
$7 \div 2\sqrt{3} - \sqrt{5}$


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Answer 1

Step-by-step explanation:

$\frac{7}{2 \sqrt{3} - \sqrt{5} } \\ \\ \frac{7}{2 \sqrt{3} - \sqrt{5} } \times \frac{2 \sqrt{3} + \sqrt{5} }{2 \sqrt{3} + \sqrt{5} } \\ \\ \frac{7(2 \sqrt{3} + \sqrt{5} ) }{(2 \sqrt{3}) {}^{2} - ( \sqrt{5} ) {}^{2} } \\ \\ \frac{7(2 \sqrt{3} + \sqrt{5} )}{(4 \times 3) - 5} \\ \\ \frac{7(2 \sqrt{3} + \sqrt{5} )}{12 - 5} \\ \\ \frac{7(2 \sqrt{3} + \sqrt{5} )}{7} \\ \\ (2 \sqrt{3} + \sqrt{5} ) \: \: \: \: \: ans$