" Evaluate ":(7sqrt(3))/(sqrt(10)+sqrt(3))-(3sqrt(2))/(sqrt(15)+3sqrt(2))-(2sqrt(5))/(sqrt(6)+sqrt(5))

For (1)/(asqrt(x)+bsqrt(y)) the rationalising factor is a asqrt(x)-bsqrt(y) . If x=(7sqrt(3))/(sqrt(10)+sqrt(3))-(3sqrt(2))/(sqrt(15)+3sqrt(2))-(2sqrt(5))/(sqrt(6)+sqrt(5)) , then value of x^(4)+x^(2) is

(2sqrt(7))/(sqrt(5)-sqrt(3))

Simplify: (7sqrt(3))/(sqrt(10)+sqrt(3))-(2sqrt(5))/(sqrt(6)+sqrt(5))-(3sqrt(2))/(sqrt(15)+3sqrt(2))

(3sqrt(2))/(sqrt(3)+sqrt(6))-(4sqrt(3))/(sqrt(6)+sqrt(2))+(sqrt(6))/(sqrt(3)+sqrt(2))

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

Simplify the following :(5sqrt(5))/(sqrt(11)+sqrt(6))-(3sqrt(3))/(sqrt(6)+sqrt(3))-(3sqrt(2))/(sqrt(15)+3sqrt(2))

Simplify (i) (4+ sqrt(5))/(4-sqrt(5))+(4-sqrt(5))/(4+sqrt(5)) (ii) (1)/(sqrt(3) + sqrt(2)) - (2)/(sqrt(5)-sqrt(3)) -(2)/(sqrt(2) - sqrt(5)) (iii) (2+sqrt(3))/(2-sqrt(3)) + (2-sqrt(3))/(2+sqrt(3)) + (sqrt(3)-1)/(sqrt(3)+1) (iv) (2+sqrt(6))/(sqrt(2)+sqrt(3))+(6sqrt(2))/(sqrt(6)+sqrt(3)) -(8sqrt(3))/(sqrt(6)+sqrt(2))

Evaluate (sqrt(5)-sqrt(3))/(sqrt(2)+sqrt(7))

(3sqrt(2))/(sqrt(6)-sqrt(3))+(2sqrt(3))/(sqrt(6)+2)-(4sqrt(3))/(sqrt(6)-sqrt(2))