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Lesson 1, Topic 1
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# Introduction – Surds

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Some numbers can be expressed as ratios of two integers, e.g $$\frac {a}{b}$$ where a and b are integers and b≠0, such numbers are called rational numbers. Examples of rational numbers.

Examples of rational numbers. $$\scriptsize 3, \; \normalsize \frac {2}{5}, \; \scriptsize 2.7 \; e.t.c$$

Other numbers cannot be expressed as ratios of integers. Such numbers are called irrational numbers. They are irrational because their exact values are not determinable, only the approximate values can be known e.g $$\scriptsize \pi$$

Surds are irrational numbers. They are the roots of rational numbers whose values cannot be expressed as exact fractions.

Examples of irrational numbers: $$\scriptsize \sqrt {3}, \; \sqrt {12}, \; \sqrt {18} \; e.t.c$$

Rules of Surds:

i. $$\scriptsize \sqrt {ab} = \sqrt{a} \: \times \: \sqrt{b}$$

ii. $$\sqrt { \frac{a}{b}} = \frac {\sqrt {a}}{\sqrt {b}}$$

iii. $$\scriptsize \sqrt {a + b} \neq \sqrt{a} \: + \: \sqrt {b}$$

iv. $$\scriptsize\sqrt {a \: – \: b} \neq \sqrt{a}\: – \: \sqrt {b}$$

Note, all values of a, b > 0.

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