Evaluate : `(15)/(sqrt(10)+sqrt(20)+sqrt(40)-sqrt(5)-sqrt(80)),` is being given that `sqrt(5)=2. 236` and `sqrt(10)=3.1362`

Explanation

`(15)/(sqrt10+sqrt20+sqrt40-sqrt5-sqrt80)`
`=(15)/(sqrt10+2sqrt5+2sqrt10-sqrt5-4sqrt5)`
`=(15)/(3sqrt10-3sqrt5)`
`=(15(3sqrt10+3sqrt15))/((3sqrt10-3sqrt15)(3sqrt10-3sqrt15))`
`=(15(3sqrt10+3sqrt15))/((3sqrt10)^2-(3sqrt5)^2)`
`=(45sqrt10+45sqrt5)/(90-45)`
`=(45(sqrt10+sqrt5))/45`
`=3.162+2.236`
`=5.398`