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))`

Explanation

(i) `(11+sqrt(11))\ (11-\ sqrt(11))`
we know,
`(a+b)(a-b)=(a^2-b^2)`
`(11+sqrt11)(11-sqrt11)=(11^2-(sqrt11)^2)`
`=121-11=110`
(ii) `(5+sqrt(7))(5-sqrt(7))`
we know,
`(a+b)(a-b)=(a^2-b^2)`
`(5+sqrt7)(5-sqrt7)=(5^2-(sqrt7)^2)`
`=25-7=18`
(iii) `(sqrt(8)-sqrt(2))\ (sqrt(8)+\ sqrt(2))`
we know,
`(a+b)(a-b)=(a^2-b^2)`
`(sqrt8+sqrt2)(sqrt8-sqrt2)=((sqrt8)^2-(sqrt2)^2)`
`=8-2=6`