`a,` `1/(√3-2)`
`=` `(√3+2)/[(√3+2)(√3-2)]`
`=` `(√3+2)/(3-2)`
`=` `(√3+2)/1`
`=` `√3``+``2`
`b,` `7/(2√3+√5)`
`=` `[7(2√3-√5)]/[(2√3+√5)(2√3-√5)]`
`=` `[7(2√3-√5)]/[(12-5)]`
`=` `[7(2√3-√5)]/7`
`=` `2√3``-``√5`
`c,` `(3√5-2√2)/(2√5-3√2)`
`=` `[(3√5-2√2)(2√5+3√2)]/[(2√5+3√2)(2√5-3√2)]`
`=` `(30+9√10-4√10-12)/(20-18)`
`=` `(18+5√10)/2`
`d,` `2/[√(7-2√6)]`
`=` `2/[√(√6-2√6+1)]`
`=` `2/[√(√6-1)^2]`
`=` `2/|√6-1|`
`=` `2/(√6-1)`
`=` `[2(√6+1)]/[(√6+1)(√6-1)]`
`=` `(2√6+2)/5`