How do black holes join each other?

Question

If black holes can swallow any object, and can radiate energy, then how could black holes join each other and can form bigger black holes?

Answer 1

If black holes can swallow any object,

Black holes have a very strong gravitational field, this field from a distance attracts any other matter and the Newtonian approximation when there is a distance is adequate. When two strong gravitational fields get close enough General Relativity equations have to be used, but the "attraction" is there and very strong.

and can radiate energy,

The energy is radiated in gravitational waves as the two black holes fall on each other. It is the radiated energy that does not allow one black hole to rotate in a stable orbit around the other, because they keep loosing energy and collapse into each other.

then how could black holes join each other and can form bigger black holes?

As the LIGO event showed it has happened, and the gravitational waves were detected and fitted by the general relativity equation. About five percent of the summed masses went into radiation, the rest built up the new single black hole.

Analysis of the signal along with the inferred redshift suggested that it was produced by the merger of two black holes with masses of 36+5/−4 times and 29±4 times the mass of the Sun (in the source frame), resulting in a post-merger black hole of 62±4 solar masses.1 The mass–energy of the missing 3.0±0.5 solar masses was radiated away in the form of gravitational waves.[2]