The root is:
kh – r – j
خ – ر – ج
It conveys the meaning of ‘going or being outside’.
Here are the English equivalents of the words with the root kh – r – j.
خرج kharaja – he went out (of the house)
خارج khaarij – outside
مخرج makhraj – exit
استخراج istikhraaj – extraction (e.g. of oil, coal)
خارجية khaarijiyya – external affairs (pol.)