Which of `(sqrt15 + sqrt3) and (sqrt10 + sqrt8)` is greater ?

Explanation

We have `(sqrt15 + sqrt3)^(2) = (sqrt15)^(2) + 2 xx sqrt15 xx sqrt3 + (sqrt3)^(2)`
`= 15 + 2 sqrt45 + 3 = 18 + 2 xx sqrt45`
Again, we have `(sqrt10 + sqrt8)^(2) = (sqrt10)^(2) + 2 xx sqrt10 xx sqrt8 + (sqrt8)^(2)`
`= 15 + 2 sqrt45 + 3 = 18 + 2 xx sqrt45`
Again, we have `(sqrt10 + sqrt8)^(2) = (sqrt10)^(2) + 2 xx sqrt10 xx sqrt8 + (sqrt8)^(2)`
`= 10 + 2 xx sqrt(10 xx 8) + 8`
`= 18 + 2 sqrt80`
Now, `sqrt80 gt sqrt45 , :. (sqrt10 + sqrt8)^(2) gt (sqrt15 + sqrt3)^(2)`
`rArr (sqrt10 + sqrt8) gt (sqrt15 + sqrt3)`
Hence between `(sqrt10 + sqrt8) and (sqrt15 + sqrt3), (sqrt10 + sqrt8)` is greater