Education Technology

Irrational Thoughts

Activity Overview

Students explore the connection between the prime factorization of a number and its surd representation. The activity is scaffolded by successive selection of appropriate numbers to help students make this connection.


ACMNA186 - Investigate the concept of irrational numbers, including π


  • Rational
  • Irrational
  • Integer
  • Surd

About the Lesson

Students start with the prime factorisation of 12 = 2 x 2 x 3 and the corresponding surd representation. Seeing the similarity between the surd representation and the prime factorisation leads students to see ‘square root’ as ‘undoing’ the squared factor. The second group of questions changes the order to make this connection slightly more challenging. Numbers such as 24 = 2 x 2 x 2 x 3 where factors are cubed implicitly connects an understanding of index laws. The algebraic functionality of the calculator encourages students to consider positive and negative square roots.