A2400 ch1i | Version 1.1 | September 2020
Simplifying surds
A LEVEL LINKS
Scheme of work: 1a. Algebraic expressions – basic algebraic manipulation, indices and surds
Key points
• A surd is the square root of a number that is not a square number,
for example etc.
• Surds can be used to give the exact value for an answer.
•
•
• To rationalise the denominator means to remove the surd from the denominator of a fraction.
• To rationalise you multiply the numerator and denominator by the surd
• To rationalise you multiply the numerator and denominator by
Examples
Example 1 Simplify
1 Choose two numbers that are
factors of 50. One of the factors
must be a square number
2 Use the rule
3 Use
Example 2 Simplify
1 Simplify and . Choose
two numbers that are factors of 147
and two numbers that are factors of
12. One of each pair of factors must
be a square number
2 Use the rule
3 Use and
4 Collect like terms
2, 3, 5,
ab a b=´
aa
bb
=
a
b
b
a
bc+
bc-
50
50 25 2=´
25 2
52
52
=´
=´
=
ab a b=´
25 5=
147 2 12-
147 2 12
49 3 2 4 3
-
=´-´
49 3 2 4 3=´-´
73223=´ -´´
73 43=-
33=
147
212
ab a b=´
49 7=
42=
