((2)/(3)sqrt(7)-(1)/(2)sqrt(2)+6sqrt(11))" and "((1)/(3)sqrt(7)+(3)/(2)sqrt(2)-sqrt(11))

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))

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 .

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

Let z_(1)=(2sqrt(3)+ i6sqrt(7))/(6sqrt(7)+ i2sqrt(3))" and "z_(2)=(sqrt(11)+ i3sqrt(13))/(3sqrt(13)- isqrt(11)) . Then |(1)/(z_1)+(1)/(z_2)| is equal to

Simplify each of the following : (i)(sqrt(2)+1)/(sqrt(2)-1)+(sqrt(2)-1)/(sqrt(2)+1)" "(ii)(sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3))+(sqrt(5)-sqrt(3))/(sqrt(5)+sqrt(3))" "(iii)(2)/(sqrt(5)+sqrt(3))+(1)/(sqrt(3)+sqrt(2))-(3)/(sqrt(5)+sqrt(2))" "(iv)(sqrt(7)+sqrt(5))/(sqrt(7)-sqrt(5))-(sqrt(7)-sqrt(5))/(sqrt(7)+sqrt(5))

Simplify each of the following : (i)(sqrt(2)+1)/(sqrt(2)-1)+(sqrt(2)-1)/(sqrt(2)+1)" "(ii)(sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3))+(sqrt(5)-sqrt(3))/(sqrt(5)+sqrt(3))" "(iii)(2)/(sqrt(5)+sqrt(3))+(1)/(sqrt(3)+sqrt(2))-(3)/(sqrt(5)+sqrt(2))" "(iv)(sqrt(7)+sqrt(5))/(sqrt(7)-sqrt(5))-(sqrt(7)-sqrt(5))/(sqrt(7)+sqrt(5))

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-

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-

(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