simplify
`(3+sqrt5)/(3-sqrt5) + (3-sqrt5)/(3+sqrt5)`

(3+sqrt5)^2 xx (3-sqrt5)^2 = ?

Find sqrt(2+3sqrt(-5)) + sqrt(2-3sqrt(-5))

Simplify: (sqrt(5)-2)/(sqrt(5)+2)-(sqrt(5)+\ 2)/(sqrt(5)-\ 2)

Simplify: (sqrt 3 - sqrt 5)(sqrt 5+ sqrt 3)

Find (sqrt 3 - sqrt 5)(sqrt 5+ sqrt3)

Simplify: (i) (7+3\ sqrt(5))/(3+\ sqrt(5))-(7-3\ sqrt(5))/(3-\ sqrt(5)) (ii) 1/(2+sqrt(3)\ )+2/(sqrt(5)-\ sqrt(3))+1/(2-\ sqrt(5))

Simplify each of the following by rationalising the denominator; 1/(5+sqrt(2)) (ii) (5+sqrt(6))/(5-sqrt(6)) (iii) (7+3sqrt(5))/(7-3sqrt(5)) (iv) (2sqrt(3)-sqrt(5))/(2sqrt(2)+3sqrt(3))

Rationales the denominator and simplify: (i) (sqrt(3)-\ sqrt(2))/(sqrt(3)\ +\ sqrt(2)) (ii) (5+2\ sqrt(3))/(7+4\ sqrt(3))

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

Simplify: (2sqrt(3)+sqrt(5))(2sqrt(3)-sqrt(5))