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Scheme of work: 1a. Algebraic expressions – basic algebraic manipulation, indices and surds you multiply the numerator and denominator by the surd b. This current work – Surds Explained with Worked Examples – offers 130+ worked examples . 22 SECTION 8: CONJUGATES & RATIONALISATION . GCSE (1 – 9). Surds. Name: Instructions. • Use black ink or ball-point pen. • Answer all questions. • Answer the questions in the spaces provided. – there may be C1: Surds. Learning objectives. After studying this chapter, you should be able to: ? distinguish between rational and irrational numbers. ? understand what is Surds are square roots of numbers which don't simplify into a whole (or rational) number: e.g. 414213 .12. ? but it is more accurate to leave it as a surd: 2. 5H Revision on Surds. Rules of Surds: ab. a b. = and a a b b. = 1. Simplify the following surds: a. 12 b. 20 c. 18 d. 27 e. 8 f. 24 g. 28 h. 32 i. 45 j. 48 k. 44 l. 63 m. In other words, if the product of two surds is rational, then each is called a rationalizing factor of the other and each is said to be rationalized by the other. For complex surds where the surds are in order 2, conjugates are used to rationalize the surds. This comes the from the formula a2?b2=(a+b)(a?b). understand the difference between surds and whole-number roots;. • simplify expressions involving surds;. • rationalise fractions with surds in the denominator. Contents. 1. . Instead, we use a technique called rationalisation. This changes. Rationalization of denominators. Simple surds. If the denominator is a simple surd, the game is easy, as illustrated by the following examples: 1. 2. Conjugate. Before calculators it was easy to look certain things up in a table, but when the surd is part of a denominator it become difficult.