应该
yīnggāi · HSK 2
should
应 = should/respond + 该 = ought; together 'ought to / should'
应 carries the sense of 'respond/ought' and 该 means 'ought/that one'. Stacked, 应该 reinforces obligation: 'should, ought to'. Compare 应当 (yīngdāng), same idea with 当 'should' as the second half.
应 — 广 (shelter) + 心 (heart) + 隹 (bird)
Originally written 應, this character combined a phonetic component with 心 (heart) to suggest 'responding from the heart' or 'answering a call'. The simplified form 应 keeps the top portion. Over time it broadened from 'respond/answer' to also mean 'should' or 'ought to'.
该 — speech radical 訁/讠 + 亥 (hài, phonetic)
该 is a phono-semantic compound. The speech radical 讠 (言) hints at meaning related to words or speaking, while 亥 supplies the sound (close to 'hài/gāi'). Originally it meant 'to be complete' or 'to encompass,' and later shifted to mean 'ought to' or 'this/that' in modern usage.