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.Without using a calculator, estimate √20 × √12, giving your answer to the nearest whole number.
(a)240
(b)12
(c)8
(d)15
2.Work out 6² − 4².
(a)2
(b)52
(c)20
(d)4
3.Work out 3³ + 2⁴.
(a)35
(b)25
(c)43
(d)432
4.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
5.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
6.Work out ∛(−27) + ∛8
(a)5
(b)−5
(c)−1
(d)−6
7.Work out the exact value of √(2² + 3²)
(a)13
(b)√5
(c)5
(d)√13
8.Work out √225 ÷ 3.
(a)8.7
(b)5
(c)75
(d)45
9.Work out ⁴√16
(a)4
(b)8
(c)64
(d)2
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
11.4ˣ = 64. Work out the value of x.
(a)16
(b)3
(c)4
(d)6
12.Work out √(4 × 9)
(a)5
(b)18
(c)36
(d)6
13.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
14.Simplify ⁴√(16a⁸b¹²)
(a)2a²b³
(b)2a⁴b⁶
(c)4a²b³
(d)2a²b⁴
15.Work out ⁴√81
(a)3
(b)20.25
(c)4.5
(d)9

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