Simplify the following expressions: `(i)\ (4+\ sqrt(7))\ (3+sqrt(2))` `(ii)\ (3+sqrt(3))\ (5-sqrt(2))` `(iii)\ (sqrt(5)-2)\ (sqrt(3)-sqrt(5))`

Explanation

(i) `(4+\ sqrt(7))\ (3+sqrt(2))`
By Distributive property, `(a+b)(c+d)=ac+ad+bc+bd`
`(4+sqrt7)(3+sqrt2)=4xx3+4sqrt2+sqrt7xx3+sqrt7xxsqrt2`
`=12+4sqrt2+3sqrt7+sqrt14`
(ii) `(3+sqrt(3))\ (5-sqrt(2))`
By Distributive property, `(a+b)(c-d)=ac-ad+bc-bd`
`(3+sqrt3)(5-sqrt2)=3xx5-3sqrt2+sqrt3xx5-sqrt3xxsqrt2`
`=15-3sqrt2+5sqrt5-sqrt6`
(iii) `(sqrt(5)-2)\ (sqrt(3)-sqrt(5))`
By Distributive property, `(a-b)(c-d)=ac-ad-bc+bd`
`(sqrt5-2)(sqrt3-sqrt5)=sqrt5xxsqrt3-sqrt5xxsqrt5-2xxsqrt3+2xxsqrt5`
`=sqrt15-5-2sqrt3+2sqrt5`