Rational and irrational numbers
Practise online with Next and Previous buttons, worked explanations and a report of the questions to review.
Log in to continueTell exact fractions, square roots and π apart, and recognise irrational lengths.
One-question preview
Choose one answer
Try this sample, or continue to the online quiz for a practice set with Next and Previous buttons.
Which number is irrational? Compare √2, 2/4, √9, 2.25.
Show worked steps
Answer: √2
- 2 is not a perfect square, so √2 is irrational.
- The other choices are fractions, terminating decimals or square roots of perfect squares.
This is a question from this topic’s quiz. Preview answers are not saved.
Scratchpad
Working out
Draw with a finger, pen or mouse, or type your working below.
Your working stays on this page. It is not submitted or saved, and clears when you leave or reload.
Curriculum reference
Victorian Curriculum F–10 Version 2.0
Pi Leo practice scope
Tell exact fractions, square roots and π apart, and recognise irrational lengths.
Read the official VCAA curriculum description (VC2M8N01)
These quizzes practise concepts within this topic. Multiple-choice answers alone do not demonstrate drawing, conducting an investigation or using a digital tool.
- VC2M8N01-C01Distinguish rational and irrational numbers.
- VC2M8N01-C02Recognise irrational numbers in measurement contexts.
- VC2M8N01-C03Recognise irrational π multiples in circle measurements.
- VC2M8N01-C04Apply and explain rational and irrational numbers using read and connect representations.
- VC2M8N01-C05Apply and explain rational and irrational numbers using calculate and explain each step.
- VC2M8N01-C06Apply and explain rational and irrational numbers using build and check a model.
- VC2M8N01-C07Apply and explain rational and irrational numbers using compare evidence and check a claim.
Learn with worked examples
Help with this topic
Skills in this topic
Traceable coverage
Subskills
These practice subskills map to the curriculum topic. Guided activities cover skills beyond multiple-choice questions.
Descriptor-derived subskills
- D01Can this number be a fraction?Distinguish rational and irrational numbers.
- D02Keep exact lengths exactRecognise irrational numbers in measurement contexts.
- D03Recognise π in an exact lengthRecognise irrational π multiples in circle measurements.
- D04Read and connect representationsApply and explain rational and irrational numbers using read and connect representations.
- D05Calculate and explain each stepApply and explain rational and irrational numbers using calculate and explain each step.
- D06Build and check a modelApply and explain rational and irrational numbers using build and check a model.
- D07Compare evidence and check a claimApply and explain rational and irrational numbers using compare evidence and check a claim.