Slove `(sqrt(11)-2)/(sqrt(11)+2)`

In each of the following determine rational number a\ a n d\ b : (i)\ (sqrt(11)-sqrt(7))/(sqrt(11)+\ sqrt(7))=a-bsqrt(77) (ii)\ (4+3sqrt(5))/(4-3sqrt(5))=a+bsqrt(5)

Which of the following is greater? 9/(sqrt(11)-sqrt(2)),9/(3sqrt(3))

Simplify the following expressions: (i) (11+sqrt(11))(11-sqrt(11)) (ii) (5+sqrt(7))(5-sqrt(7)) (iii) (sqrt(8)-sqrt(2))(sqrt(8)+sqrt(2)) (iv) (sqrt(7)-3)(sqrt(7)+3)

Simplify the following expressions. (i) (5+sqrt(7))(2+sqrt(5)) (ii) (5+sqrt(5))(5-sqrt(5)) (iii) (sqrt(3)+sqrt(7))^2 (iv) (sqrt(11)-sqrt(7))(sqrt(11)+sqrt(7))

Simplify the following expressions: (i)\ (11+sqrt(11))\ (11-\ sqrt(11)) (ii)\ (5+sqrt(7))(5-sqrt(7)) (iii)\ (sqrt(8)-sqrt(2))\ (sqrt(8)+\ sqrt(2))

Rationalise the denominator in each of the following : i) 2/7 (ii) 2/(3sqrt(3)) (iii) (2sqrt(7))/(sqrt(11))

Solve for x: sqrt(11x-6)+sqrt(x-1)=sqrt(4x+5)

Show that : (3sqrt(2)-2sqrt(3))/(3sqrt(2)+2sqrt(3))+(2sqrt(3))/(sqrt(3)-sqrt(2))=11

Rationalise the denominator in each of the following: (i) 2/(sqrt(7)) (ii) 2/(3sqrt(3)) (iii) (2sqrt(7))/(sqrt(11))

Sum of 1/(sqrt(2)+sqrt(5))+1/(sqrt(5)+sqrt(8))+1/(sqrt(8)+sqrt(11))+1/(sqrt(11)+sqrt(14))+..to n terms= (A) n/(sqrt(3n+2)-sqrt(2)) (B) 1/3 (sqrt(2)-sqrt(3n+2) (C) n/(sqrt(3n+2)+sqrt(2)) (D) none of these