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Simplifying surds | Pearson, Study Guides, Projects, Research of Algebra

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.

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2021/2022

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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+
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=
pf3

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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

  1. One of each pair of factors must be a square number 2 Use the rule 3 Use and 4 Collect like terms

ab = a ´ b

a a b (^) b

a b

b

a b + c

b - c

ab = a ´ b

ab = a ´ b

Practice questions 1 Simplify. a b c d e f g h 2 Simplify. a b c d e f Answers 1 a b c d e f g h 2 a b c d

Hint One of the two numbers you choose at the start must be a square number. Watch out! Check you have chosen the highest square number at the start.