`(sqrt(2)-sqrt(8))/(sqrt(2)+sqrt(8))`

The value of sqrt(( sqrt(12) -sqrt(8))(sqrt(3)+sqrt(2))/(5+sqrt(24)) is

(sqrt(8)+sqrt(3))/(sqrt(8)-sqrt(3))+ (sqrt(8)-sqrt(3))/(sqrt(8)+sqrt(3))

The following are the steps involved in finding the value of x-y from (sqrt(8)-sqrt(5))/(sqrt(8)+sqrt(5))=x-ysqrt(40) . Arrange them in sequential order. (A) (13-2sqrt(40))/(8-5)=x-ysqrt(40) (B) ((sqrt(8))^(2)+(sqrt(5))^(2)-2(sqrt(8))(sqrt(5)))/((sqrt(8))^(2)-(sqrt(5))^(2))=x-ysqrt(40) (C) x-y=(11)/(3) (D) x=(13)/(3) and y=(2)/(3) (E) ((sqrt(8)-sqrt(5))(sqrt(8)-sqrt(5)))/((sqrt(8)+sqrt(5))(sqrt(8)-sqrt(5)))=x-ysqrt(40)

1/(1-sqrt(2))+ 1/(sqrt(2)-sqrt(3))+1/(sqrt(3)-sqrt(4))+..........+1/(sqrt(8)-sqrt(9))

Simplify (sqrt(11)+sqrt(8))(sqrt(11)-2sqrt(2))

(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(8))

The simplest form of (sqrt(8+sqrt28)-sqrt(8-sqrt(28)))/(sqrt(8+sqrt(28))+sqrt(8-sqrt(28)))