Question with 国 on-yomi

Dictionaries state the On-yomi for 国 is コク, but when you write, 中国 (China), the hirigana needed becomes: ちゅう・ごく.

Is this an irregular kanji? How would a person know that kou becomes goku?

Same with 学, how does a person know the pronounciation changes from ガク to がっ when used to say 小学校.

Thanks in advance!

FYI, I am new to the language, just started studying 2 weeks ago.

The altered pronunciation of 国 in 中国 is part of a phenomenon called rendaku. To summarize the article, if a word is written in kanji, you cannot know for sure whether rendaku occurs or not; there is no hard rule that covers all the cases. You just have to learn it word by word - you can guess based on common patterns, but may still be surprised when turning to a dictionary for confirmation. For example with 忠告, even though the individual characters have the same readings as 中 and 国 respectively, it's pronounced ちゅうこく, not -ごく.

On the other hand, "...ku" followed by "k..." turning into "...っk..." (as in がく + こう -> がっこう) is a quite common and predictable pattern which simply makes the word easier to pronounce. Other examples include 突っ込む (つく + こむ -> つっこむ) and 却下 (きゃく + か -> きゃっか).

Thank you lanthas. That was extremely helpful!

Sorry for nitpicking, but 突っ込む is the euphonic change(促音便) of 突き込む, not 突く込む, as same as 引っ掻く(from 引き掻く), おっぱらう(from 追い払う), 掘っ立て小屋(from 掘り立て小屋).