I suggested he buy the dictionary. How come the verb buy must be in root word ? Explain and provide more examples. Thanks.

That's because it's the subjunctive mood.
The following [verbs + "that"] often attract (for lack of a better word) the subjunctive mood: "ask," "command," "demand," "determine," "insist," "order," "prefer," "recommend," "require," and "suggest." And these [adjectives + "that"] do likewise: "crucial," "essential," "important," "imperative," and "necessary."
With either the aforementioned verbs or adjectives, we use the base form of the verb (the way the verb would appear as a dictionary entry, i.e., without -s, -ed, or -ing), regardless of the noun or pronoun.
Here are some more examples:
1. The teacher suggested that Peter go (not “goes”) to study hall after class to get help in geometry.
2. I insist that Nan put (not “puts”) her phone away before the exam starts.
3. The editor said it was essential that Henry meet (not “meets”) the deadline.
4. We demand that this post end (not “ends”) soon.

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