Find `sqrt4/3 times sqrt4/3 times sqrt4/3 times sqrt4/3`

The locus of the point of intersection of the lines sqrt3 x- y-4sqrt3 t= 0 & sqrt3 tx +ty-4 sqrt3=0 (where t is a parameter) is a hyperbola whose eccentricity is: (a) sqrt3 (b) 2 (c) 2/sqrt3 (d) 4/3

Simplify {(\sqrt 5+\sqrt 3)\times (\sqrt 5 - \sqrt 3)}/(\sqrt 7- \sqrt 3)\times (\sqrt 7+ \sqrt 3)/(\sqrt 7+\sqrt 3)

Simplify: (\sqrt 5+\sqrt 3)/(\sqrt 5 - \sqrt 3)\times (\sqrt 5+\sqrt 3)/(\sqrt 5 +\sqrt 3)

Simplify : (\sqrt 5 - \sqrt 3)/(\sqrt 3 + \sqrt 5) \times (\sqrt 5 - \sqrt 3)/(\sqrt 3 -\sqrt 5)

(1)/(sqrt(3))times(sqrt(2))/(sqrt(3))=

(sqrt(2)+sqrt(3))times(sqrt(3)+sqrt(8))

sqrt3 xx sqrt3

Simplify: 1/(sqrt5 + sqrt4) + 1/(sqrt4 + sqrt3) + 1/(sqrt3 + sqrt2) + 1/(sqrt2 + sqrt1)

Prove that cot 7 ""(1^(@))/(2) = sqrt2 + sqrt3 + sqrt4 + sqrt6 = (sqrt3 + sqrt2) (sqrt2 +1 ).

Prove that tan 7 (1^(@))/(2) = sqrt2 - sqrt3 -sqrt4 + sqrt6 = (sqrt3 - sqrt2) (sqrt2 -1).