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

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

Add 2sqrt(2)+5sqrt(3) and sqrt(2)-3sqrt(3) .

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))

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

Simplify: (i) (3sqrt(2)-2sqrt(2))/(3sqrt(2)+\ 2sqrt(3))+(sqrt(12))/(sqrt(3)-\ sqrt(2)) (ii) (sqrt(5)+\ sqrt(3))/(sqrt(5)-\ sqrt(3))+(sqrt(5)-\ sqrt(3))/(sqrt(5)+\ sqrt(3))

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

Simplify each of the following by rationalising the denominator: (7+3sqrt(5))/(7-3sqrt(5)) (ii) (2\ sqrt(3)-\ sqrt(5))/(2sqrt(2)+\ 3sqrt(3))

Simplify the following expressions: (i) (4+sqrt(7))(3+sqrt(2)) (ii) (3+sqrt(3))(5-sqrt(2)) (iii) (sqrt(5)-2)(sqrt(3)-sqrt(5)) (iv) (sqrt(5)+sqrt(2))(sqrt(3)+sqrt(2))

Find the number of terms in the following expansions. ( sqrt(3) + sqrt(5) )^(7) ( sqrt(3) - sqrt(5) )^(7)

The value of sqrt(5+2sqrt(6)) is (a) sqrt(3)-sqrt(2) (b) sqrt(3)+sqrt(2) (c) sqrt(5)+sqrt(6) (d) none of these