# OCR, Unit B Higher Surds notes

very easy to understand surds notes

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GCSE Notes and Revision Surds

See videos : http://www.waldomaths.com/video/Surds01/Surds01.jsp + +

Rules of surds

(1) Multiplication a b ab , eg. 2 3 6

a a 10 10

(2) Division , eg. 5

b b 2 2

(3) Squaring and rooting ( a ) 2 a , eg. 7 7 ( 7) 2 7

a2 a , eg. 36 62 6

Simplifying surd expressions

(A) It is normal to make the number inside the square root sign as small as

possible

Example 1: Simplify 12 .

Answer: 12 4 3 4 3 2 3 2 3 (In other words, factorise the

number and take out any factors which are square numbers and square root them.

The number left in the square root sign has no more square factors)

Example 2: Simplify 108 .

Answer: 108 9 12 9 4 3 3 2 3 6 3

Questions 1: Simplify: (a) 18 (b) 48 (c) 50 (d) 84

(e) 90 (f) 98 (g) 132 (h) 200 (i) 52

(B) You can simplify multiples to a single surd expression

Example 1: Simplify 2 3 Answer: 6

Example 2: Simplify 6 10 Answer: 6 10 60 4 15 2 15

Example 3: Simplify 26 39 Answer: 2 13 3 13 6 132 13 6

Questions 2: Simplify: (a) 6 15 (b) 10 15 (c) 14 21

(C) You can add or subtract expressions if they are multiples of the same surd

Example 1: 3 2 5 2 8 2

Example 2: 18 8 3 2 2 2 2

Questions 3: Simplify: (a) 40 10 (b) 27 12 (c) 24 6

(d) 125 75 (e) 44 99

(D) It is usual to "rationalise the denominator". In other words, if there is a surd in

the denominator of a fraction, simplify so that the only surds appear in the numerator.

2 2 2 3 2 3

Example 1: Simplify Answer: (notice

3 3 3 3 3

that although the answer seems less simple, there are no surds in the denominator)

21 21 14 21 14 3 14

Example 2: Simplify Answer:

14 14 14 14 2

Copyright © R F Barrow 2005-2010

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