`(1-sqrt-1)(1+sqrt-1)(5-sqrt-7)(5+sqrt-7)`=?

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

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

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-

Simplify the following expressions: (i) (11+sqrt(11))(11-sqrt(11)) (ii) (5+sqrt(7))(5-sqrt(7)) (iii) (sqrt(8)-sqrt(2))(sqrt(8)+sqrt(2)) (iv) (sqrt(7)-3)(sqrt(7)+3)

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

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))

sqrt(5){(sqrt(5)+1)^(50)-(sqrt(5)-1)^(50)}

If log_(7)log_(7) sqrt(7sqrt(7sqrt(7)))=1-a log_(7)2 and log_(15)log_(15) sqrt(15sqrt(15sqrt(15sqrt(15))))=1-b log_(15)2 , then a+b=

Simplify the following expressions: (i)\ (11+sqrt(11))\ (11-\ sqrt(11)) (ii)\ (5+sqrt(7))(5-sqrt(7)) (iii)\ (sqrt(8)-sqrt(2))\ (sqrt(8)+\ sqrt(2))

The value of sqrt(2-1)/sqrt(2)+3-2sqrt(2)/(4)+(5sqrt2-7/6)sqrt(2)+17-12sqrt(2)/(16)+..+++..+ add.infty is