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.Work out ⁴√81
(a)3
(b)20.25
(c)4.5
(d)9
2.Work out ∛(−27) + ∛8
(a)5
(b)−5
(c)−1
(d)−6
3.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
4.Simplify ⁴√(16a⁸b¹²)
(a)2a²b³
(b)2a⁴b⁶
(c)4a²b³
(d)2a²b⁴
5.Given that 2⁵ = 32, work out 2⁶.
(a)34
(b)37
(c)192
(d)64
6.Work out −(−3)⁴ + (−3)³
(a)−108
(b)54
(c)−54
(d)108
7.Work out the value of 6² − 4³.
(a)100
(b)28
(c)−28
(d)0
8.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
9.Work out 5⁰ + 5¹ + 5²
(a)125
(b)30
(c)31
(d)35
10.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
11.Work out ⁴√16
(a)4
(b)8
(c)64
(d)2
12.Work out √225 ÷ 3.
(a)8.7
(b)5
(c)75
(d)45
13.Without using a calculator, estimate √20 × √12, giving your answer to the nearest whole number.
(a)240
(b)12
(c)8
(d)15
14.√700 lies between which two consecutive integers?
(a)35 and 36
(b)7 and 8
(c)25 and 26
(d)26 and 27
15.4ˣ = 64. Work out the value of x.
(a)16
(b)3
(c)4
(d)6

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