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

Express each one of the following with rational denominator: (i) (sqrt(3)+\ 1)/(2sqrt(2)-\ sqrt(3)) (ii) (6-4sqrt(2))/(6+4sqrt(2))

Express each one of the following with rational denominator: (sqrt(3)+1)/(2sqrt(2)-sqrt(3))( ii) (6-4sqrt(2))/(6+4sqrt(2))

Simplify (i) (4+ sqrt(5))/(4-sqrt(5))+(4-sqrt(5))/(4+sqrt(5)) (ii) (1)/(sqrt(3) + sqrt(2)) - (2)/(sqrt(5)-sqrt(3)) -(2)/(sqrt(2) - sqrt(5)) (iii) (2+sqrt(3))/(2-sqrt(3)) + (2-sqrt(3))/(2+sqrt(3)) + (sqrt(3)-1)/(sqrt(3)+1) (iv) (2+sqrt(6))/(sqrt(2)+sqrt(3))+(6sqrt(2))/(sqrt(6)+sqrt(3)) -(8sqrt(3))/(sqrt(6)+sqrt(2))

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

Find the angles of the triangle whose sides are (sqrt(3)+1)/(2sqrt(2)), (sqrt(3)-1)/(2sqrt(2)) and sqrt(3)/2 .

If S=[((sqrt(3)-1)/(2sqrt(2)),(sqrt(3)+1)/(2sqrt(2))),(-((sqrt(3)+1)/(2sqrt(2))),(sqrt(3)-1)/(2sqrt(2)))], A=[(1,0),(-1,1)] and P=S ("adj.A") S^(T) , then find matrix S^(T) P^(10) S .

If S=[((sqrt(3)-1)/(2sqrt(2)),(sqrt(3)+1)/(2sqrt(2))),(-((sqrt(3)+1)/(2sqrt(2))),(sqrt(3)-1)/(2sqrt(2)))], A=[(1,0),(-1,1)] and P=S ("adj.A") S^(T) , then find matrix S^(T) P^(10) S .

If S=[((sqrt(3)-1)/(2sqrt(2)),(sqrt(3)+1)/(2sqrt(2))),(-((sqrt(3)+1)/(2sqrt(2))),(sqrt(3)-1)/(2sqrt(2)))], A=[(1,0),(-1,1)] and P=S ("adj.A") S^(T) , then find matrix S^(T) P^(10) S .

If S=[((sqrt(3)-1)/(2sqrt(2)),(sqrt(3)+1)/(2sqrt(2))),(-((sqrt(3)+1)/(2sqrt(2))),(sqrt(3)-1)/(2sqrt(2)))], A=[(1,0),(-1,1)] and P=S ("adj.A") S^(T) , then find matrix S^(T) P^(10) S .