Printable · GCSE Higher · ages 14-16
Powers and roots worksheet — GCSE Higher
Fifteen questions on "powers and roots" — DfE statement N6. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.
part Higher
Powers and roots worksheet — GCSE Higher
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- 1.Given that 4³ = 64 and 5³ = 125, estimate ∛100 to 1 decimal place.
- 2.Work out √(4 × 9)
- 3.Work out ∛64.
- 4.The mass of a radioactive sample, in grams, n years after it was first weighed is modelled by M = 200 × (1/2)ⁿ. Work out the mass the model gives after 3 years.
- 5.By first working out 2.9², then squaring your result, estimate 2.9⁴ to 2 significant figures.
- 6.Work out the exact value of √(2² + 3²)
- 7.Work out ⁴√16
- 8.By considering fourth powers, work out which two consecutive integers ⁴√200 lies between.
- 9.A cube-shaped storage box has edges of length 7 cm. A shelf can hold a total volume of 2,000 cm³. Work out the greatest number of these boxes that will fit in that volume.
- 10.Without using a calculator, estimate √20 × √12, giving your answer to the nearest whole number.
- 11.Work out 3³ + 2⁴.
- 12.Work out 6² − 4².
- 13.Given that 5³ = 125 and 6³ = 216, use a midpoint test to estimate ∛130 to 1 decimal place.
- 14.Given that 2⁵ = 32, work out 2⁶.
- 15.√700 lies between which two consecutive integers?
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