Surds -- simplifying, multiplying, dividing, and adding/subtracting

Simplify surds using the largest perfect-square factor, multiply and divide surds by combining under one root, add and subtract like surds, and rationalise a denominator.

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Te reo Māori terms

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Learning objective overview

Master Teaching Guide coverage for this objective.

Resources

Terminology

  • Surd
  • Radicand
  • Simplify
  • Rationalise
  • Like surds
  • Perfect square

Task goals

  • Identify whether a number is a surd (an irrational root left in exact form).
  • Simplify a surd by finding its largest perfect-square factor.
  • Multiply and divide surds by combining them under one root, then simplify.
  • Add and subtract like surds (matching radicand) by collecting them as like terms.
  • Rationalise the denominator of a fraction containing a surd.

Key skills

  • Surds
  • Simplifying surds
  • Multiplying dividing surds
  • Adding subtracting surds
  • Rationalise denominator

Quick stats

  • 0 total questions
  • 3 difficulty levels
  • Answers included
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