Find and check all numerical solutions
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Use numerical guess-check-and-refine to solve x² = 2 for x > 0. Give x to two decimal places.
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Answer: 1.41
- Find consecutive integers whose squares bracket 2.
- Refine the interval with decimal trial values.
- The positive solution rounds to 1.41.
- √(2) ≈ 1.414214.
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Curriculum reference
Victorian Curriculum F–10 Version 2.0
Pi Leo practice scope
Use graphing and systematic refinement while checking the search interval and number of roots.
Read the official VCAA curriculum description (VC2M10A16)
These quizzes practise concepts within this topic. Multiple-choice answers alone do not demonstrate drawing, conducting an investigation or using a digital tool.
Activities to practise beyond the quiz
- Supported by the guided activity; selecting an MCQ does not demonstrate this action.
- Supported by the guided activity; selecting an MCQ does not demonstrate this action.
- VC2M10A16-C01Use changing trial values to locate a root to a stated precision.
- VC2M10A16-C02Implement numerical guess-check-and-refine using digital tools.
- VC2M10A16-C03Use symmetry, algebra and a wider graph to check completeness.
- VC2M10A16-C04Use digital graphs and numerical reasoning to assess whether all solutions were found.
- VC2M10A16-C05Apply and explain find and check all numerical solutions using calculate and explain each step.
- VC2M10A16-C06Apply and explain find and check all numerical solutions using read and connect representations.
- VC2M10A16-C07Apply and explain find and check all numerical solutions using compare evidence and check a claim.
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Subskills
These practice subskills map to the curriculum topic. Guided activities cover skills beyond multiple-choice questions.
Descriptor-derived subskills
- D01Bracket and refineUse changing trial values to locate a root to a stated precision.
- D02A found root may not be the only rootUse symmetry, algebra and a wider graph to check completeness.
- D03Calculate and explain each stepApply and explain find and check all numerical solutions using calculate and explain each step.
- D04Read and connect representationsApply and explain find and check all numerical solutions using read and connect representations.
- D05Compare evidence and check a claimApply and explain find and check all numerical solutions using compare evidence and check a claim.