ALG020 · Algebraic expressions · Classes 9–11
Surds
A surd is an irrational root such as √2 or √3. Surds are kept exact by simplifying them and combining like surds.
√48 = 4√3Surds
📐 Formula
√a × √b = √(ab); a√c + b√c = (a + b)√c
✏️ Worked example
√48 = √(16 × 3) = 4√3 ≈ 6.93.
🌍 Where it is used
Exact lengths in geometry and trigonometry (sin 60° = √3/2).
❓ Quick check
√2 × √8 = ?
🏋️ Practice
EasySimplify √20.
Answer: 2√5
Medium2√3 + 5√3 = ?
Answer: 7√3
ChallengeRationalise 1/√2.
Answer: √2/2