Put squares, cubes, roots and estimates together, and test yourself.
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Tick what you can now do after this chapter.
Cards for the key terms and rules from this chapter.
Questions from easy to hard across the chapter.
Which of the following numbers can potentially be a perfect square based on its unit digit?
Decide which expression is greatest, and explain why.
Which of the following differences is the greatest? Explain your reasoning.
Identify the expression with the largest value.
Focus on comparing the rate of change for cubes vs. squares, and larger bases vs. smaller bases.
Guess cube roots without factorising.
You are told the following numbers are perfect cubes: 1331, 4913, 12167, and 32768.
Guess their cube roots without prime factorization.
Provide the cube roots in the same order as the prompt numbers.
Explain how you used unit digits and bounding (multiples of 10) to find the exact roots.
Think about when prime factorisation is the best method.
Consider the two primary methods we used in this chapter:
Which was more challenging? Why?
State clearly which approach you found harder.
Give a specific reason or a common mistake you encountered.
Describe a scenario where estimating a square root is faster or more useful than factoring it completely.