Theoretically, yes you can grown plant from roots based on the "Totipotency" theory. There are many reports regenerating plants from root callus. Hairy roots are different from normal roots in many ways. If you could make appropriate growing medium to induce callus from the hairy roots then you will be able to regenerate the plants.

The principals of tissue culture tech show that any meristematic tissue could do the job. in your case with basil you have to try your self since the metabolites constituent in your plant tissue may interfere when seeking for bright callus and in turn good seedlings

I agree with Rajasekaran Palanisamy, he explained in the simple manner n it is true tooo....

Hi, Maryam Zare. The big problem that not any plant can grow from any meristimatic tissue - the is a lot of different reasons for it. Practice is a often a way different then a theory.

In order to grow a new plant from meristimatic tissue you have to search Google for "tissue culture protocols + name of the plant". You have to use those protocols or you may end up spending years developing your own (and probably you would not be able to do it without extensive experience).

P.S. Hairs in the roots does not contain meristem - hairs are just modified cells. Tip of the topical root does contain meristematic tissue. But other parts of the plant may give you better results - such as apical meristem or lateral buds.

As the above colleagues says, regenerate a plant from a hairy root is a big challenge.

Http://www.ncbi.nlm.nih.gov/pubmed/14963692

i hope this will help.