Radha is nowhere mentioned in Mahabharat, Vishnu Puran, Bhagavat Puran. Some people claim that she is mentioned indirectly. May be, but the name "Radha" for a gopi nowhere finds direct mention in any of these books. Mahabharat does talk about Radha, but this Radha is Karn's foster-mother and not the gopi Radha.
However Radha does find mention in Padm Puran and very detailed mention in Brahm Vaivart Puran.
The reason Krishna-Radha are worshipped is that there is not as much story of the love between Krishna and Rukmini as between Krishna and Radha. The poet Jayadev popularised this love in his Gita-Govindam. Later, many people popularised the love between Krishna and Radha even more.
Those who worship Krishna and Radha say that there are various forms of Lord Vishnu. In four-handed form, he is present in Vaikuntha. This is the form, which people usually mean when they use the word "Vishnu". However, he is also present in two-handed form in Golok. This form is called Krishna. Both Golok and Vaikunth are eternal and are in spiritual world. So, Krishna incarnation happened on Earth in which Krishna lived on Earth for 125 years. Also, Krishna lives eternally in Golok. In Vaikunth, Vishnu lives eternally with Laxmi. In Golok, Krishna lives eternally with Radha.
It is also said that in Saket dham, Lord Rama lives eternally with Sita.