Correct Answer - D
Let `B-=(alpha,beta)`, where `alpha,beta` are rational.
Given `HA^2=HB^2`
`rArr(3-sqrt2)^2+(5-sqrt5)^2=(alpha-sqrt2)^2+(beta-sqrt5)^2`
`41-6sqrt2-10sqrt5=alpha^2+beta^2+7-2sqrt2alpha-2sqrt5beta`
`rArr alpha^2+beta^2-34++2(3-alpha)sqrt2+2(5-beta)sqrt5=0`
Since `alpha` and `beta` are rational,
`3-alpha=0rArralpha=3`
and `5-beta=0rArrbeta=5`
`therefore AB=0`