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

We can multiply whole numbers together. e.g. 4×6= 24 We can multiply surds together. e.g. 3 × 2 = 6 But we cannot multiply whole numbers and surds together. e.g. 8× 5 = 8 5

Similarly we can divide whole numbers. e.g. 18 2 = 9 We can divide surds. e.g. 10 2 = 5 But we cannot divide whole numbers and surds. e.g. 15 3

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

Examples: 4) 56 2 5) 6 48 2 3 = 56 2 =3 48 3 = 28 =3 16 = 4 × 7 =3×4 =2 7 =12

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