Express each one of the following with rational denominator:
(i)`(30)/(5sqrt(3)-3 sqrt(5))` (ii) `1/(2sqrt(5)- sqrt(3)) `

Explanation

(i) `30/(5sqrt3-3sqrt5)xx(5sqrt3+3sqrt5)/(5sqrt3+3sqrt5)`
`(30(5sqrt3+3sqrt5))/(25xx3-9xx5)`
`(30(5sqrt3+3sqrt5))/30`
`5sqrt3+3sqrt5`
`(ii) 1/((2sqrt5)-(sqrt3))`
`1/((2sqrt5)-(sqrt3))xx((2sqrt5)+(sqrt3))/((2sqrt5)+(sqrt3))`
`((2sqrt5)+(sqrt3))/((2sqrt5)^2-(sqrt3)^2)`
`((2sqrt5)+(sqrt3))/(4xx5-3)`
`((2sqrt5)+(sqrt3))/(20-3)`
`((2sqrt5)+(3))/(17)`