the oo in booger and the ur in burger are not the same. English has 14 seperate vowels. the vowel for booger is a top back vowel closely related to the oo in moon.. It is a little further back in the mouththan oo in moon and isfounfd in the word book.
.. The vowel ur in burger is a centralized vowel and is found in girl or the last vowel in burger.
Look up "English vowel chart" for the positions of the tip of the tongue that determine in part the sounds of the vowels.
BTW, burger is a meat patty,
booger is nasal excrement
'and bugger (a completely different vowel from the other two) is an insulting word'
John