Left 木 (tree) — the indexing radical. Roots are tree-anatomy, so the wood-radical sets the semantic stage: 根 belongs with 枝 (branch), 叶 (leaf), 干 (trunk). The tree on the left, root meaning below ground, anchored to its source.
Right 艮 supplies the sound (gěn → gēn, just a tone shift) and a strong semantic resonance: 艮 means 'stubborn, fixed in place' — exactly what roots do. Phonetic family: 跟 (heel), 痕 (scar), 很 (very) — all on 艮, all with a 'stuck-fast' nuance.