Simplify : `( 1/2 + 1 - 2/sqrt3)/ ( 2/sqrt3 + 1/2 +1)`

Simiplify : (-(1)/(2)- (sqrt3)/(2)i)^(2)

Simplify: ((-1)/(2)- (sqrt3)/(2)i)^(2)

Simplify : (22)/(2sqrt(3)+1)+(17)/(2sqrt(3)-1)

Simplify: (sqrt3/2)^2 -(sqrt3)^2+(sqrt 2)^2 +1/2

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

if x = 2 - sqrt3 , find x^2 + 1/x^2

Rationalize the denominator: (2 + sqrt 3)/(2 - sqrt 3) + (2 - sqrt 3)/(2 + sqrt 3) + (sqrt 3 - 1)/(sqrt 3 + 1)

Simplify : (1)/(sqrt(3)+sqrt(2))-(1)/(sqrt(3)-sqrt(2))+(2)/(sqrt(2)+1)

Simplify : 7sqrt((1)/(3)) -2(1)/(3) sqrt((1)/(3)) +3 sqrt( 147)

The sum of (1)/( 2sqrt1+1 sqrt2 ) + (1)/( 3 sqrt2 + 2 sqrt3 ) + (1)/( 4 sqrt3 + 3 sqrt4 ) +...+(1)/( 25 sqrt 24 + 24 sqrt25) is