This study notes covers Worked Example 2: Adding Surds within Surds for GCSE Mathematics. Revise Surds in Number for GCSE Mathematics with 14 exam-style questions and 22 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 8 of 15 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.
Worked Example 2: Adding Surds
Simplify: √12 + √27
Solution
First simplify each surd:
√12 = √(4×3) = 2√3
√27 = √(9×3) = 3√3
Now add like surds:
2√3 + 3√3 = 5√3
Answer: 5√3
Practice questions for Surds
Which of these is the simplified form of √48?
Explain why it is preferable to write fractions in rationalized form rather than leaving a surd in the denominator.
Quick recall flashcards
What are Like Surds?
Surds with the same root part
Examples of like surds:
• 3√2 and 5√2 (both have √2)
• 2√7 and -4√7 (both have √7)
Can add/subtract like surds:
3√2 + 5√2 = 8√2
What is a surd?
An irrational root that cannot be simplified to a whole number
Examples: √2, √3, √5, ∛7
NOT surds: √4 = 2, √9 = 3 (these simplify to whole numbers)