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This lecture covers the concept of roots of real numbers, starting with positive roots and moving on to real roots. The instructor explains properties of roots, such as raising a number to a power and taking roots of roots. Various examples are provided to illustrate the properties and how to solve equations involving roots. The lecture also delves into the significance of positive and negative roots, as well as the extension of notation to include negative numbers. Theoretical aspects are complemented with practical examples to demonstrate the application of the concepts discussed.