Review of representation of natural numbers

Integers

Rational numbers on the number line

Representation of terminating / non-terminating recurring decimals, on the number line through successive magnification

Rational numbers as recurring/terminating decimals

Examples of non-recurring / non-terminating decimals

Existence of non-rational numbers (irrational numbers) such as √2, √3 and their representation on the number line

Explaining that every real number is represented by a unique point on the number line and conversely, every point on the number line represents a unique real number

Existence of √x for a given positive real number x (visual proof to be emphasized)

Definition of nth root of a real number

Recall of laws of exponents with integral powers

Rational exponents with positive real bases (to be done by particular cases, allowing learner to arrive at the general laws)

Rationalization (with precise meaning) of real numbers of the type 1/(a+b√x) and 1/(√x+√y) (and their combinations) where x and y are natural number and a and b are integers