`sqrt 5 (1+sqrt5)x = 2 sqrt5 + 4`

(sqrt2 + 1)/sqrt5

The value of { 1/(sqrt6 - sqrt5) - 1/(sqrt5 - sqrt4) + 1/(sqrt4 - sqrt3) - 1/(sqrt3 - sqrt2) + 1/(sqrt2 - 1)} is :

(2 + sqrt5)/(2 - sqrt5)

Prove that sin 9^circ = 1/4 (sqrt(3 + sqrt5) - sqrt(5 - sqrt5)) .

Prove that sin 27^circ = 1/4 (sqrt(5 + sqrt5) - sqrt(3 - sqrt5)) .

Evaluate : ( sqrt5 - sqrt2 ) times ( sqrt5 + sqrt2 )