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 HigherNon-calculator

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Powers and roots worksheet — GCSE Higher

Maths · GCSE Higher · N6 · Powers and roots · Non-calculator · 15 questions

MathsUKwww.geekhero.co.uk

1.Given that 4³ = 64 and 5³ = 125, estimate ∛100 to 1 decimal place.
(a)4.7
(b)5.0
(c)4.6
(d)4.5
2.Work out 6² − 4².
(a)2
(b)52
(c)20
(d)4
3.Work out 5⁰ + 5¹ + 5²
(a)125
(b)30
(c)31
(d)35
4.Work out 3³ + 2⁴.
(a)35
(b)25
(c)43
(d)432
5.Work out √(4 × 9)
(a)5
(b)18
(c)36
(d)6
6.By considering fourth powers, work out which two consecutive integers ⁴√200 lies between.
(a)14 and 15
(b)4 and 5
(c)3 and 4
(d)5 and 6
7.Work out ∛(−27) + ∛8
(a)5
(b)−5
(c)−1
(d)−6
8.Work out −(−3)⁴ + (−3)³
(a)−108
(b)54
(c)−54
(d)108
9.Work out ⁴√81
(a)3
(b)20.25
(c)4.5
(d)9
10.Without using a calculator, estimate the value of √70 × ∛65, giving your answer to 1 significant figure.
(a)10
(b)30
(c)40
(d)50
11.4ˣ = 64. Work out the value of x.
(a)16
(b)3
(c)4
(d)6
12.Work out the value of 6² − 4³.
(a)100
(b)28
(c)−28
(d)0
13.Simplify ⁴√(16a⁸b¹²)
(a)2a²b³
(b)2a⁴b⁶
(c)4a²b³
(d)2a²b⁴
14.Work out ∛64.
(a)21.3
(b)4
(c)192
(d)8
15.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

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