1.
eradication; extermination; total destruction
Complete elimination of something down to the roots, leaving nothing behind. Often used for destroying a group, family line, or population entirely.
A compound of 根 (root) and 絶やし (extinguishing, from 絶やす — to cut off). The image is of pulling up every root so nothing can grow back. A vivid, strong word implying total and merciless destruction.
Usage
Almost always used in the pattern ～を根絶やしにする (to wipe out ~). Carries a harsh, dramatic tone. Common in historical narratives, war contexts, and figurative usage about completely eliminating something.