`=(- sqrt(5) +- sqrt(11))/4`

Simplify: (4+\ sqrt(5))/(4-sqrt(5))+(4-\ sqrt(5))/(4+\ sqrt(5))

Write in ascending order: 3 sqrt(5) and 4 sqrt(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))

Evalutate : (4-sqrt(5))/(4+sqrt(5))+ (4+sqrt(5))/(4-sqrt(5))

The perpendicular distance from the origin to the plane containing the two lines, (x+2)/3=(y-2)/5=(z+5)/7 and (x-1)/1=(y-4)/4=(z+4)/7 is: (a) 11sqrt6 (b) 11/(sqrt6) (c) 11 (d) 6sqrt(11)

a=9-4sqrt(5) , sqrt(a)-1/sqrt(a)=?

Evaluate using binomial theorem: (i) (sqrt(2)+1)^(6) +(sqrt(2)-1)^(6) (ii) (sqrt(5)+sqrt(2))^(4)-(sqrt(5)-sqrt(2))^(4)

Rationalise the denominator and simplify: (i) (4sqrt(3)+5sqrt(2))/(sqrt(48)+\ sqrt(18)) (ii) (2sqrt(3)-\ sqrt(5))/(2\ sqrt(2)+\ 3sqrt(3))

Obtain other zeroes of the polynomial p(x)=2x^4-x^3-11x^2+5x+5 if two of its zeroes are sqrt(5) and -sqrt(5) .

Obtain other zeroes of the polynomial p(x)=2x^4-x^3-11x^2+5x+5 if two of its zeroes are sqrt(5) and -sqrt(5) .