(15)/(4sqrt(3)-3sqrt(2))+(7)/(6sqrt(3))+5sqrt(2)

Rationales the denominator and simplify: (sqrt(3)-sqrt(2))/(sqrt(3)+sqrt(2)) (ii) (5+2sqrt(3))/(7+4sqrt(3)) (iii) (1+sqrt(2))/(3-2sqrt(2)) (2sqrt(6)-sqrt(5))/(3sqrt(5)-2sqrt(6)) (v) (4sqrt(3)+5sqrt(2))/(sqrt(48)+sqrt(18)) (vi) (2sqrt(3)-sqrt(5))/(2sqrt(3)+3sqrt(3))

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))

Add (i) (2sqrt(3)-5sqrt(2)) and (sqrt(3) + 2sqrt(2)) (ii) (2sqrt(2) + 5sqrt(3) - 7 sqrt(5) and (3sqrt(3)-sqrt(2) + sqrt(5)) (iii) ((2)/(3) sqrt(7) -(1)/(2)sqrt(2)+6sqrt(11)) and ((1)/(3)sqrt(7) + (3)/(2)-sqrt(11))

(3sqrt(2))/(sqrt(6)-sqrt(3))-(4sqrt(3))/(sqrt(6)-sqrt(2))-(6)/(sqrt(8)-sqrt(12))=? a.sqrt(3)-sqrt(2)b*sqrt(3)+sqrt(2)c.5sqrt(3)d.1

Show that : (1)/(3-2sqrt(2))- (1)/(2sqrt(2)-sqrt(7)) + (1)/(sqrt(7)-sqrt(6))-(1)/(sqrt(6)-sqrt(5))+(1)/(sqrt(5)-2)=5 .

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

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

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

Prove that (i) (1)/(3+sqrt(7)) + (1)/(sqrt(7)+sqrt(5))+(1)/(sqrt(5)+sqrt(3)) +(1)/(sqrt(3)+1)=1 (ii) (1)/(1+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(4))+(1)/(sqrt(4)+sqrt(5))+(1)/(sqrt(5)+sqrt(6))+(1)/(sqrt(6)+sqrt(7)) +(1)/(sqrt(7)+sqrt(8))+(1)/(sqrt(8) + sqrt(9)) = 2