0580

Surds

Number

Exact values

  • A surd is a root that cannot be written as a whole number or a fraction, because the number underneath is not a perfect power
    • √7 is a surd, whereas √49 is simply 7
Root 2, root 13, root 99 and root 201 labelled as surds, set against root 16, the root of two thirds and the root of 6.23, which are not: 16 is a square number so its root is 4, while two thirds and 6.23 are not integers
Source: Surds & exact values by Save My Exams
  • Surds are irrational: their decimal form never ends and never repeats
  • Leaving an answer as a surd keeps it exact, whereas a rounded decimal is only an approximation
  • Rounding partway through a calculation and continuing loses accuracy, so surds are carried through the working and evaluated last, if at all