Is validating the results of an article important before citing such an article? During writing my academic paper, I need to cite accuracy values of cited research paper.

I have been advised that if you will cite a paper, you need to read that paper entirely. But in this case, Do i need to validate results that they achieved.
Reading yes. It is important to avoid extraction of sentences or results which can be less general than as they appear at the first glance. 

Validating not at all, unless you feel you must do it because something is suspicious or you think to deal with a particular or new case.

You can't validate each statement for every cited reference, and you can't do so for several reasons.
Also a referee does not. Papers exists to be used. That is an implicit form of validation.