应该

yīng gāi

ought to; should; must

yīng

to agree (to do sth)

gāi

should

agree (应) + owe a response (该) = ought to

应 carries an old sense of responding or agreeing to an obligation; 该 pairs speech (讠) with a phonetic element (亥) to mean what is owed or due. Together they reinforce each other: what you have agreed to and what is owed is what you should do.

你累了,应该好好休息一下。

nǐ lèi le, yīng gāi hǎo hǎo xiū xi yī xià.

You are tired; you should rest well for a bit.

做错了事,应该主动向对方道歉。

zuò cuò le shì, yīng gāi zhǔ dòng xiàng duì fāng dào qiàn.

If you have done something wrong, you ought to take the initiative to apologize to the other person.