# OCR, Unit B Higher 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
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
14 14 14 14 2

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Questions 4: Simplify: (a) (b) (c)
5 3 3
3 6 12 21 2 15 12 3 6 2
(d) (e) (f) (g)
3 6 12 6
(E) Multiplying brackets with surd expressions. Initially you should treat the surd
expression like an algebraic expression, and simplify after multiplying the brackets.…read more