Powers and roots worksheet — GCSE Higher

1.Work out ∛64.

2.Without using a calculator, estimate √20 × √12, giving your answer to the nearest whole number.

3.Given that 2⁵ = 32, work out 2⁶.

4.Given that 5³ = 125 and 6³ = 216, use a midpoint test to estimate ∛130 to 1 decimal place.

5.Work out √225 ÷ 3.

6.Work out 5⁰ + 5¹ + 5²

7.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.

8.Work out ⁴√16

9.Work out the value of 6² − 4³.

10.Given that 4³ = 64 and 5³ = 125, estimate ∛100 to 1 decimal place.

11.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?

12.√700 lies between which two consecutive integers?

13.Work out −(−3)⁴ + (−3)³

14.Work out ∛(−27) + ∛8

15.Work out ⁴√81