expression, noun-modifying (irregular)
Prenominal expression meaning something is so absurd or foolish that it deserves laughter or mockery. Often used in the pattern 笑うべき話 (a laughable story) or 笑うべき間違い (a ridiculous mistake).
それは笑うべき間違いだ。
That's a laughable mistake.
彼の言い訳は笑うべきものだった。
His excuse was ridiculous.
笑える is a more colloquial, standalone adjective meaning 'funny' or 'laughable,' while 笑うべき is a literary, prenominal form emphasizing that something should be laughed at.
おかしい is a general adjective for 'funny' or 'strange,' whereas 笑うべき specifically implies something is worthy of ridicule or laughter.
Formed from the verb 笑う (to laugh) + the classical auxiliary adjective べき (should), functioning as a prenominal modifier meaning 'should be laughed at.'