As you probably already know the “trigger” for an “H-Bomb” is an “A-Bomb” located inside. Two or three more “Tsar Bomba” size tests and we’d all probably be dead.
Twists and turn to that one. Tsar Bomba was designed to be 100mt, but was modified to be between 50-58mt. And almost its entire force was from fusion, so it made very little fallout, especially being detonated at about 4km as an air burst.
So, if it was popped at full force in a ground burst, it would be far more dirty and dangerous, but it is still questionable that three of them could wipe out mankind.