Simplifying Surds
√50 = ?
50 = 25 × 2
√50 = √(25×2)
= √25 × √2
= 5√2
Always find largest square!
Like Surds
Can add: 2√3 + 5√3 = 7√3
(like 2x + 5x = 7x)
Can't add: √2 + √3
(different surds)
First simplify, then combine!
Difference of Squares
(a + √b)(a - √b) = a² - b
Example:
(3 + √2)(3 - √2)
= 9 - 2
= 7
No surd in answer!
This diagram covers Visual Understanding 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 6 of 15 in this topic. Focus on the labels, the relationships between parts, and the explanation that turns the diagram into an exam-ready answer.
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.