[" Simplify: "],[qquad 8.quad (sqrt(5)+sqrt(3))/(sqrt(80)+sqrt(48)-sqrt(45)-sqrt(27))]

Simplify: (sqrt(5)+sqrt(3))/(sqrt(80)+sqrt(48)-sqrt(45)-sqrt(27))

(4sqrt(3)+5sqrt(2))/(sqrt(48)+sqrt(18))

For (1)/(asqrt(x)+bsqrt(y)) the rationalising factor is a asqrt(x)-bsqrt(y) . If x=(sqrt(5)+sqrt(3))/(sqrt(80)+sqrt(48)-sqrt(45)-sqrt(27)) then value of 4x^(2)+3x+5 is

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

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

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

simplify (sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3))-(sqrt(5)-sqrt(3))/(sqrt(5)+sqrt(3))

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

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