Question

What would be the denominator after rationalizing 1 / ( 2√5-√3 ) ?

Answer 1

$\frac{1}{2 \sqrt{5} - \sqrt{3} } \\ \\ = \frac{1}{2 \sqrt{5} - \sqrt{3} } \times \frac{2 \sqrt{5} + \sqrt{3} }{2 \sqrt{5} + \sqrt{3} } \\ \\ = \frac{2 \sqrt{5} + \sqrt{3} }{( {2 \sqrt{5}) }^{2} - {( \sqrt{3}) }^{2} } \\ \\ = \frac{2 \sqrt{5} + \sqrt{3} }{4 \times 5 - 3} \\ \\ = \frac{2 \sqrt{5} + \sqrt{3} }{20 - 3} \\ \\ = \frac{2 \sqrt{5} + \sqrt{3} }{17}$

After rationalizing the denominator will be 17