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.Work out ∛64.
- 2.Work out ⁴√81
- 3.Work out ∛(−27) + ∛8
- 4.Four students each estimate √70 without a calculator. Ben says: '8² = 64 and 9² = 81, and 70 is about a third of the way from 64 to 81, so √70 ≈ 8.3.' Chloe says: '8.5² = 72.25, which is close to 70 but a little too big, so I'll bring it down slightly to √70 ≈ 8.4.' Dan says: '9² = 81 is closer to 70 than 8² = 64 is, so √70 ≈ 8.9.' Ella says: '8² = 64 and 9² = 81, so I'll just take the midpoint of 8 and 9: √70 ≈ 8.5.' Given that √70 = 8.3666... to 4 decimal places, whose estimate is closest?
- 5.Work out 3³ + 2⁴.
- 6.Work out −(−3)⁴ + (−3)³
- 7.Without using a calculator, estimate the value of √70 × ∛65, giving your answer to 1 significant figure.
- 8.4ˣ = 64. Work out the value of x.
- 9.√700 lies between which two consecutive integers?
- 10.By considering fourth powers, work out which two consecutive integers ⁴√200 lies between.
- 11.Work out ⁴√16
- 12.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.
- 13.Work out 5⁰ + 5¹ + 5²
- 14.Work out √225 ÷ 3.
- 15.Given that 4³ = 64 and 5³ = 125, estimate ∛100 to 1 decimal place.
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