Simplify `(5((1)/(2))^(2)+((1)/(sqrt(2)))^(2)-4((1)/(sqrt(3)))^(2))/(2((1)/(2))((sqrt(3))/(2))+1)`

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

Simplify: (1)/(1+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(5))

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

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

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

x=(1)/(1+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+2)=

Let A=[[cos theta,-sin theta],[sin theta,cos theta]] Find the value of A^(-50) at theta=(pi)/2 (A) [[-(sqrt(3))/(2),-(1)/(2)],[-(1)/(2),(sqrt(3))/(2)]] (B) [[(sqrt(3))/(2),(1)/(2)],[(-1)/(2),(sqrt(3))/(2)]] (C) [[-(sqrt(3))/(2),(1)/(2)],[(1)/(2),(sqrt(3))/(2)]] (D) [[(1)/(2),(sqrt(3))/(2)],[(sqrt(3))/(2),(-1)/(2)]]

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

(1)/(sqrt(3)+sqrt(2))-(2)/(sqrt(5)-sqrt(3))-(3)/(sqrt(2)-sqrt(5))

(1)/(2+sqrt(3))+(2)/(sqrt(5)-sqrt(3))+(1)/(2-sqrt(5))=0