Simplify each of the following by rationalising the denominator: `1/(5+sqrt(2))` (ii) `(5+sqrt(6))/(5-sqrt(6))`

Explanation

(i)`1/(5+sqrt(2))`
`=>1/(5+sqrt(2))xx(5-sqrt(2))/(5-sqrt(2)`
`=>(5-sqrt(2))/(25-2)`
`=>(5-sqrt(2))/23`

(ii)`(5+sqrt(6))/(5-sqrt(6))`
`=>(5+sqrt(6))/(5-sqrt(6))xx(5+sqrt(6))/(5+sqrt(6))`
`=>(5+sqrt(6))^2/(5^2-sqrt(6)^2`
`=>(25+6+2xx5xx sqrt(6))/ (25-6)`
`=>(31+10 sqrt(6))/19`