GCSE – Numeracy and Mathematics
Tier: Higher
Grade:
A/A*
Topic: Surds and irrational
numbers
Top Tips!
Starter:
1. Work out √36
2. List the first 10 square numbers
3. Write √32 in surd form
4. Write √27 in surd form
•
•
•
•
•
•
Look for factors that are square numbers when writing roots
in surd form
√𝑎 × √𝑎 = 𝑎
√𝑎 × √𝑏 = √𝑎𝑎
𝑎
√𝑎 ÷ √𝑏 = �𝑏
Treat surds like algebraic like terms 3√2 + 4√2 = 7√2
To rationalise a surd you must rationalise the denominator
E.g. 1
Rationalise
Multiply the numerator and denominator by √3
Skills:
=
1. Simplify √10 × √6. Write your
answer in surd form.
2. Simplify 3√2 × √6. Write your
answer in surd form.
3. Simplify √8 + √18. Write your
answer in surd form.
4. Rationalise
2
√3
7
√2
Assessment for Learning
E.g. 2
2×√3
√3×√3
=
2√3
√9
Rationalise
=
7
5+√2
2√3
3
Multiply the numerator and denominator by 5 − √2
=
7
(5+�2)
(5−√2)
√2)
× (5−
Examination Question:
=
7(5−√2)
(25−2)
=
7(5−√2)
23
2016 November (new) Mathematics U1 Higher Q17
Simplify
2√18
(5√3)2 −
√2
√32 × √2
and state whether your answer is rational or irrational.
Video / QR code
GCSE – Numeracy and Mathematics
Tier: Higher
Grade:
A/A*
Topic: Surds and irrational
numbers
Top Tips!
Starter:
1. Work out √36
6 (or -6)
2. List the first 10 square numbers
1, 4, 9, 16, 25, 36, 49, 64, 81,
100
3. Write √32 in surd form
4√2
4. Write √27 in surd form
3√3
•
•
•
•
•
•
Look for factors that are square numbers when writing roots
in surd form
√𝑎 × √𝑎 = 𝑎
√𝑎 × √𝑏 = √𝑎𝑎
𝑎
√𝑎 ÷ √𝑏 = �𝑏
Treat surds like algebraic like terms 3√2 + 4√2 = 7√2
To rationalise a surd you must rationalise the denominator
E.g. 1
Rationalise
Multiply the numerator and denominator by √3
Skills:
=
1. Simplify √10 × √6. Write your
answer in surd form.
E.g. 2
2√15
6√3
3. Simplify √8 + √18. Write your
answer in surd form.
4. Rationalise
𝟕√𝟐
𝟐
7
√2
2×√3
√3×√3
=
2√3
√9
Rationalise
7
5+√2
7
(5+�2)
(5−√2)
√2)
× (5−
Examination Question:
2√3
3
=
7(5−√2)
(25−2)
=
7(5−√2)
23
2016 November (new) Mathematics U1 Higher Q17
Simplify
2√18
(5√3)2 −
√2
√32 × √2
and state whether your answer is rational or irrational.
Numerator:
2
(5�3) = 5√3 × 5√3 = 25√9 = 25 × 3 = 75
2√18
√2
=
6√2
√2
=6
75 – 6 = 69
Denominator: √32 × √2 = √64 = 8
Answer:
69
8
The answer is rational as
Assessment for Learning
=
Multiply the numerator and denominator by 5 − √2
=
2. Simplify 3√2 × √6. Write your
answer in surd form.
5√2
2
√3
69
8
is a terminating decimal.
Video / QR code