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Cubes and cube roots
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EasyQuestion 1
[2 marks]Work out:
(a) 4³
(b) ∛216
Solution for Question 1
MediumQuestion 2
[3 marks]Work out:
(a) (-3)³
(b) ∛(-125)
(c) What is the difference between (-3)³ and -3³?
Solution for Question 2
HardQuestion 3
[3 marks]A cube has volume 343 cm³.
Find the surface area of the cube.
Solution for Question 3
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A cube number is the result of multiplying a number by itself three times: 1³ = 1, 2³ = 8, 3³ = 27, 4³ = 64, 5³ = 125, 10³ = 1000. You should memorise cubes up to 10³ for your GCSE.
The cube root (∛) asks "what number multiplied by itself three times gives this?" Unlike square roots, cube roots can be negative: ∛(-8) = -2 because (-2) × (-2) × (-2) = -8.
Cubes grow much faster than squares. While 10² = 100, we have 10³ = 1000. This is why cube numbers appear in volume calculations (since volume involves three dimensions).
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