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There are some basic rules when dealing with surds. Example: √36 = 6. The above roots have exact values and are called Rational. Example: √2 = 1.41. These roots do NOT have exact values and are called Irrational OR SURDS.
•understand the difference between surds and whole-number roots; •simplify expressions involving surds; •rationalise fractions with surds in the denominator.
Surds. Workout. Question 1: Work out each of the following. √3 ╳ √5 . √7 ╳ √2 . √11 ╳ √6 . (e) √8 ╳ √2 . (f) √3 ╳ √3 . (g) √5 ╳ √6 . (i) √6 ╳ √6 . (j) √10 ╳ √3 . (k) √5 ╳ √20 . (d) √2 ╳ √3 . (h) √5 ╳ √2 . (l) √11 ╳ √10 .
1. Surds and Indices. In this chapter we will learn: how to manipulate expressions involving surds, how to manipulate expressions involving indices. 1.1 Types of Number. Modern Mathematics is built on the back of thousands of years of mathematical thought. Over the centuries, mathematicians saw the need for ever more complicated ideas of number.
Operations with Surds. Numbers like √2, √3, √5 and √6 are all irrational and are called surds. To work efficiently with surds you need to know your perfect square numbers. 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256… Simplifying surds. Rules: √𝑎𝑎𝑎𝑎= √𝑎𝑎× √𝑎𝑎 𝑎𝑎 𝑏𝑏 = √ ...
Rules of surds: ab = a × b. = a a. b. these are true in both directions. i.e. × a b = ab. b a = a b. Applications: We usually want to simplify expressions involving surds. Past Paper Questions:
Definition. A surd is an irrational number resulting from a radical expression that cannot be evaluated directly. 4 8 , etc are all surds. , and can only be approximated by a decimal.
