Right 页 - the indexing radical, originally meaning head (now also page in books). Combined with the hair-strands on the left, 页 declares 须 a head-feature: the beard hanging from the face. Same head family: 顶 (top), 颈 (neck), 颜 (face), 顺 (smooth).
Left 彡 - three diagonal strokes picturing fine hairs or strands. Originally 须 pictured a face with strands hanging from the chin: a beard. From the literal beard came the verbal senses to need and must, via an old pun on the homophone 需. Same hair-tuft family: 形 (shape), 影 (shadow), 修 (groom).
