Q:

Why does the meaning of a root sound different than the root? 

I am currently constructing a language for my fantasy world.  I am utilizing roots, prefixes, suffixes - all that fun stuff.  I've noticed something that I find rather strange though.  Nearly every word root is Latin or Greek.  Nearly every definition for those roots is not.  Why is this? 
For example, the root capitmeans head.  Head sounds nothing like capit.  Why don't we just say 'capit' instead of 'head'?  I know these two words (capit and head) are from different languages.  I want to know why.  
EDIT: Posted for clarity's sake: This is the question in different terms: If we use Latin/Greek roots for a lot of our words, why does our source change from Latin to Old English (or Germanic or whatever it happens to be) for the definition of the root?  
Example: If we use the root capit to form words involving head, why don't we just call a head a capit?  Why are our roots mostly Greek and Latin, while the definitions of the roots (head, hand, love, sit, drag, voice, carry, etc.)  are not?  

A:

You need to make up one root, and define it in English.  Say you decide op means head or is the root for words that have head in them, like capit is English.  Then you can add suffixes and prefixes and such to op so that oppy or arop or tomopsoo mean things (in English) the way capital and captain and decapitate mean things to us.  Maybe the people in your world will use the word op on its own, or maybe they will have another word specifically for head, the way we do in English.  English is a really hard language to explain or invent.  Most made up languages don't try to inherit from multiple other made up languages.  Many derive from multiple real languages (eg English and French) to give an end result that's clearly different, yet somehow almost understandable.  Modesitt is especially good at this.  Others just make up a bunch of roots and then add suffixes and prefixes and infixes, as you are doing.  
As for your observation that most of our roots are not English, I suspect you're just not noticing.  Think about headache, for example.  Or headscarf.  We make tons of words from head.  The words made from capit tend to be more governmenty or intellectual - and that's about who used which languages as English grew.  

A:

English draws its lexicon from many sources: from Old English, sort of a 'cousin' of Old High German, both being derived from Proto-Germanic; from (at different times) Old and Modern French; from classical Latin (which is also ancestral to Old French) and from classical Greek. 
Head, as the comments tell you, descends from an Old English word, heafod = 'head', while the capit- stem is that of Latin caput, also = 'head'. ( The same word became chef in Old and then Modern French, from which we borrowed our word for a 'head' cook.) 
More remotely, however, all these descend from the same Proto-Indo-European word, kaput; but it has undergone different sound changes along each line of descent.