# SURDS

CONTENT

1. Meaning of rational and irrational numbers leading to the definition of surds.
2. The rules guiding the basic operation with surd i.e $$\sqrt{a} + \sqrt{b} ≠ \sqrt{a + b}$$; $$\sqrt{a} -\sqrt{b} ≠ \sqrt{a -b}$$; $$\sqrt{a} × \sqrt{b} = \sqrt{a × b}$$; $$\sqrt{a} ÷ \sqrt{b} = \sqrt{\frac{a}{b}}$$
3. Conjugates of a binomial surd using the idea of the difference of two squares
4. Application to solving triangles involving trigonometric ratios of special angles $$30^o, 60^o,$$ and $$45^o$$ .
5. Evaluation of expressions involving surds.

## Meaning of Rational and Irrational Numbers Leading to the Definition of Surds

### Rational Numbers (Fractions)

Rational numbers are any number that can be expressed as a ratio of two integers (i.e can be expressed as a fraction in the form $$\frac{a}{b}$$ where $$a$$ and $$b$$ are integers and where $$b ≠ 0$$. Any integer can be expressed as $$\frac{a}{1}$$, hence integers are rational numbers such as $$\frac{1}{3},\frac{5}{17},\frac{7}{10},\frac{-4}{7}, \frac{9}{1},$$ etc. are rational numbers. Therefore Natural numbers are subsets of Integers while Integers are subset of Rational numbers N⊂ Z ⊂ Q

Examples are:

(i) Proper and improper fractions: $$\frac{3}{4}, \frac{2}{3}$$ and $$\frac{14}{9}, \frac{17}{10}$$

(ii) Mixed numbers: $$2\frac{3}{4}, 5\frac{3}{7}$$

(iii) Integers i.e counting numbers : $$0 = \frac{0}{1}, 6\frac{6}{1}, -9 = \frac{-9}{1}$$

(iv) Terminating decimals, e.g.

Lesson tags: General Mathematics Lesson Notes, General Mathematics Objective Questions, SS3 General Mathematics, SS3 General Mathematics Evaluation Questions, SS3 General Mathematics Evaluation Questions First Term, SS3 General Mathematics First Term, SS3 General Mathematics Objective Questions, SS3 General Mathematics Objective Questions First Term
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