When ancient Greek mathematicians discovered that the diagonal of a unit square has length √2, they found a number that couldn't be written as a fraction. This discovery shook mathematics! Today, we keep these 'irrational' numbers in their exact root form - called surds - because they're more precise than any decimal approximation. Engineers use surds for exact calculations in bridge designs, physicists for quantum mechanics, and even your phone's GPS calculations involve surds.
This introduction covers The Exact Truth 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 1 of 15 in this topic. Use this introduction to connect the idea to the wider topic before moving on to questions and flashcards.
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 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)
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