Online dictionaries are great - but there i a price: your memory is not really trained. Here is how the use of dictionaries can boost your Arabic.
Al-Khalil ibn Ahmad al-Farahidi (الخليل بن أحمد الفراهيدي), a grammarian who was born in 718 (100 AH) in present-day Oman.
Google Translate is great - but unfortunately not for Arabic. There is an excellent alternative: the Google Chrome extension "Arabic Dictionary".
Episode #8 of my series "9273 roots": 20 questions for the man who coded the best desktop-app for Lane's Arabic-English Lexicon: Graeme Andrews.
Episode #3 of "9273 roots": 20 questions for Hossam Abouzahr who created the best and most up-to-date online dictionary for Arabic dialects: Lughatuna (living arabic).
A list of the best Android and iOS apps and websites for translating Arabic words into English. Most of them are free.
Actually, I don't think that anybody has ever counted the number of Arabic roots. Mathematically: 21,952 roots. Practically, you get 6,332 roots.