Squares, cubes and roots Cambridge IGCSE Mathematics (9–1) revision
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In plain words
Squaring a number is multiplying it by itself. Cubing is doing it once more. A root goes backwards: the square root of 49 asks "what times itself makes 49?" Knowing the common ones by heart saves a lot of time.
Three things to know
- Squares to know: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225. Cubes to know: 1, 8, 27, 64, 125, and 10³ = 1000.
- √49 = 7, and ∛27 = 3 because 3 × 3 × 3 = 27.
- The equation x² = 49 has two answers, 7 and −7, because a negative times a negative is positive.
Tips and tricks
- √ on its own means the positive root. But "solve x² = 49" needs both: x = ±7.
- Squaring is not doubling. 6² is 36, not 12.
It lands in your notebook with its questions as flashcards.
Squares, cubes and roots: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
What is 12²?
12 × 12.
What is the cube root of 125?
5 × 5 × 5 = 125.
What is √196?
14 × 14 = 196.
What is 4³?
4 × 4 × 4.
What are the solutions of x² = 25?
(−5)² is also 25.
Quiz
5 questions
Tap an answer and you’ll see straight away whether it’s right, and why.
Worksheet
3 questions, 6 marks. Write your answers on paper, then check them.
Squares, cubes and roots
Cambridge IGCSE Mathematics (9–1) 0980 · 6 marks · papermunch.org
Name ______________________________ Date ______________
Work out 13² and ∛64.[2]
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169 and 4.
Work out √144 + 2³.[2]
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20. 12 + 8.
Solve x² = 81.[2]
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x = 9 or x = −9.
Answers: Squares, cubes and roots
- 1. 169 and 4.
- 2. 20. 12 + 8.
- 3. x = 9 or x = −9.