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.

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Powers and roots worksheet — GCSE Higher

Maths · GCSE Higher · N6 · Powers and roots · 15 questions

MathsUKwww.geekhero.co.uk

1.Given that 2⁵ = 32, work out 2⁶.
(a)34
(b)37
(c)192
(d)64
2.By first working out 2.9², then squaring your result, estimate 2.9⁴ to 2 significant figures.
(a)71
(b)81
(c)70
(d)64
3.Work out ∛64.
(a)21.3
(b)4
(c)192
(d)8
4.Work out 6² − 4².
(a)2
(b)52
(c)20
(d)4
5.Work out ⁴√81
(a)3
(b)20.25
(c)4.5
(d)9
6.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.
(a)5.8
(b)6
(c)5
(d)343
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.
(a)12.5 g
(b)25 g
(c)0.125 g
(d)300 g
8.Simplify ⁴√(16a⁸b¹²)
(a)2a²b³
(b)2a⁴b⁶
(c)4a²b³
(d)2a²b⁴
9.Work out √225 ÷ 3.
(a)8.7
(b)5
(c)75
(d)45
10.Work out the value of 6² − 4³.
(a)100
(b)28
(c)−28
(d)0
11.√700 lies between which two consecutive integers?
(a)35 and 36
(b)7 and 8
(c)25 and 26
(d)26 and 27
12.Work out ⁴√16
(a)4
(b)8
(c)64
(d)2
13.Work out the exact value of √(2² + 3²)
(a)13
(b)√5
(c)5
(d)√13
14.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?
(a)Ben's estimate
(b)Chloe's estimate
(c)Ella's estimate
(d)Dan's estimate
15.Work out −(−3)⁴ + (−3)³
(a)−108
(b)54
(c)−54
(d)108

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