Surds Roots that are irrational are called surds. Law 1: 𝑎 𝑏 = 𝑎𝑏 Simplify 𝟑𝟐 + 𝟏𝟖 + 𝟏𝟐𝟖 , without the use of a calculator. 32 + 18 + 128 = 16×2 + 9×2 + 64×2 = 16 2 + 9 2 + 64 2 Law 1 =4 2 +3 2 +8 2 =15 2

Surds Write 𝟐𝟕 + 𝟏𝟐 in the form of k 𝟑 , where k ∈ N. 27 + 12 27 + 12 = 9×3 + 4×3 = 9 × 3 + 4 × 3 =3 3 +2 3 =5 3 If 𝟖 + 𝟓𝟎 − 𝟐 =𝒏 𝟐 , find the value of n. 8 + 50 − 2 =𝑛 2 4×2 + 25×2 − 2 =𝑛 2 4 2 + 25 2 − 2 =𝑛 2 2 2 +5 2 − 2 =𝑛 2 6 2 =𝑛 2 ∴𝑛=6