Question

rationalise the denominator of 1/2+√5

Answer 1

simply multiply numerator and denominator
by 2-√5

then

2-√5/4-5

so answer is √5-2 because 4-5=(-1),

Answer 2

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