Question

rationalise the dinominator 8÷7-3 root 5

Answer 1

given :-

8/(7 - 3√5)

$\tt = \frac{8}{7 - 3 \sqrt{5} } \times \frac{7 + 3 \sqrt{5} }{7 + 3 \sqrt{5} } \\ \\ \tt = \frac{8(7 + 3 \sqrt{5}) }{(7 - 3 \sqrt{5})(7 + 3 \sqrt{5} ) } \\ \\ \tt = \frac{56 + 24 \sqrt{5} }{( {7)}^{2} - ( {3 \sqrt{5}) }^{2} } \\ \\ \tt = \frac{56 + 24 \sqrt{5} }{49 - 45} \\ \\ \tt = \frac{56 + 24 \sqrt{5} }{4} \\ \\ \tt = \frac{(2 \times \cancel4 \times 7) + (2 \times 3 \times \cancel4) \sqrt{5} }{ \cancel4} \\ \\ \tt = \boxed{14 + 6 \sqrt{5} }$

identity used :-

» (a + b) (a - b) = a² - b²

Answer 2

Answer in the attachment:-