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.Work out √(4 × 9)
(a)5
(b)18
(c)36
(d)6
2.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
3.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
4.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
5.√700 lies between which two consecutive integers?
(a)35 and 36
(b)7 and 8
(c)25 and 26
(d)26 and 27
6.Work out ⁴√81
(a)3
(b)20.25
(c)4.5
(d)9
7.4ˣ = 64. Work out the value of x.
(a)16
(b)3
(c)4
(d)6
8.Given that 2⁵ = 32, work out 2⁶.
(a)34
(b)37
(c)192
(d)64
9.Without using a calculator, estimate √20 × √12, giving your answer to the nearest whole number.
(a)240
(b)12
(c)8
(d)15
10.Work out ⁴√16
(a)4
(b)8
(c)64
(d)2
11.Work out √225 ÷ 3.
(a)8.7
(b)5
(c)75
(d)45
12.Work out 6² − 4².
(a)2
(b)52
(c)20
(d)4
13.Work out 3³ + 2⁴.
(a)35
(b)25
(c)43
(d)432
14.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
15.Simplify ⁴√(16a⁸b¹²)
(a)2a²b³
(b)2a⁴b⁶
(c)4a²b³
(d)2a²b⁴

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