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" (1) "(1)/(3+sqrt(7))+(1)/(sqrt(7)+sqrt...

" (1) "(1)/(3+sqrt(7))+(1)/(sqrt(7)+sqrt(5))+(1)/(sqrt(5)+sqrt(3))+(1)/(sqrt(3)+1)=1

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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

Simplify (1)/(3 - sqrt(8)) - (1)/(sqrt(8) - sqrt(7)) + (1)/(sqrt(7) - sqrt(6)) - (1)/(sqrt(6) - sqrt(5)) + (1)/(sqrt(5) - 2)

(1)/(2sqrt(7)+sqrt(5))-(1)/(2sqrt(5)+sqrt(7)) simplify

(1)/(3-sqrt(8))-(1)/(sqrt(8)-sqrt(7))+(1)/(sqrt(7)-sqrt(6))-(1)/(sqrt(6)-sqrt(5))+(1)/(sqrt(5)-2)=5

(1)/(3-sqrt(8))-(1)/(sqrt(8)-sqrt(7))+(1)/(sqrt(7))-sqrt(6))-(1)/(sqrt(6)-sqrt(5))+(1)/(sqrt(5)-2)=5

(1)/(3-sqrt(8))-(1)/(sqrt(8)-sqrt(7))+(1)/(sqrt(7)-sqrt(6))-(1)/(sqrt(6)-sqrt(5))+(1)/(sqrt(5)-2)=5

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 .

( Show that: )/(3-sqrt(8))-(1)/(sqrt(8)-sqrt(7))+(1)/(sqrt(7)-sqrt(6))-(1)/(sqrt(6)-sqrt(5))+(1)/(sqrt(5)-2)=5

Evaluate : (1)/(3-sqrt(8)) -(1)/(sqrt(8)-sqrt(7))+(1)/(sqrt(7)-sqrt(6))-(1)/(sqrt(6)-sqrt(5))+(1)/(sqrt(5)-2).