Prove that `(1)/(sqrt(7))=(1)/(sqrt(7))times(sqrt(7))/(sqrt(7))`

Prove that: 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 .

(3-sqrt7)(3+sqrt7)=?

Prove that: 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

1/(sqrt(7)+sqrt(3))\times (sqrt(7)-sqrt(3))/(sqrt(7)-sqrt(3))

Show that: 1/(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).

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

(sqrt(7)+2sqrt(3))(sqrt(7)-2sqrt(3))

Rationalise the denominator in each of the following: (i) 2/(sqrt(7)) (ii) 2/(3sqrt(3)) (iii) (2sqrt(7))/(sqrt(11))