1. Surds 2 Multiplying & Dividing
Millburn Academy
Maths department
National 5
Surds 2 Multiplying & Dividing

2. We can multiply whole numbers together.
e.g. 4×6= 24
We can multiply surds together.
e.g × 2 = 6
But we cannot multiply whole numbers and surds together.
e.g. 8× 5 =
8 5

3. Similarly we can divide whole numbers.
e.g = 9
We can divide surds.
e.g = 5
But we cannot divide whole numbers and surds.
e.g

4. which can be simplified
Examples:
1) 7 × 2
3) 6 × 2
which can be simplified
= 14
= 12
= 4 × 3
2) 4 5 ×2 3
=2 3
=8 15

5. Examples: 4) 5) = =
= 28
=3 16
= 4 × 7
=3×4
=2 7
=12

6. Rules:
𝑥 × 𝑦
= 𝑥𝑦
𝑎 𝑥 ×𝑏 𝑦
=𝑎𝑏 𝑥𝑦
= 𝑥 𝑦
𝑥 𝑦
= 𝑎 𝑏 𝑥 𝑦
𝑎 𝑥 𝑏 𝑦