Question

rationalise 8/√15+1-√5-√3

Answer 1

Hello Mate!

$\frac{8}{ \sqrt{15} + 1 - \sqrt{5} - \sqrt{3} } \\ can \: we \: write \: it \: as \\ \frac{8}{ \sqrt{15} + 1 - ( \sqrt{5} + \sqrt{3} )} \\ conjucate = \\ \frac{8}{( \sqrt{15} + 1) - ( \sqrt{5} + \sqrt{3} )} \times \frac{( \sqrt{15} + 1) + ( \sqrt{5} + \sqrt{3} )}{( \sqrt{15} + 1) + ( \sqrt{5} + \sqrt{3}) } \\ \frac{8( \sqrt{5} + \sqrt{3} )}{ {( \sqrt{15} + 1)}^{2} - {( \sqrt{5} + \sqrt{3}) }^{2} } \\ \frac{8( \sqrt{5} + \sqrt{3}) }{15 + 1 - 5 - 3} \\ \frac{8( \sqrt{5} + \sqrt{3} )}{8} = \sqrt{5 } + \sqrt{3}$

Hope it helps☺!