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

VersionsA only A + B A + B + Csame questions, different order

AnswersQuestions only With answer key Key only

CalculatorMixed Non-calculator (Paper 1)Calculator (Papers 2 and 3)

New sheet

Powers and roots worksheet — GCSE Higher

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

MathsUKwww.geekhero.co.uk

1.Work out the exact value of √(2² + 3²)
(a)13
(b)√5
(c)5
(d)√13
2.√700 lies between which two consecutive integers?
(a)35 and 36
(b)7 and 8
(c)25 and 26
(d)26 and 27
3.Work out ⁴√16
(a)4
(b)8
(c)64
(d)2
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.Work out the value of 6² − 4³.
(a)100
(b)28
(c)−28
(d)0
6.Work out 3³ + 2⁴.
(a)35
(b)25
(c)43
(d)432
7.Work out 6² − 4².
(a)2
(b)52
(c)20
(d)4
8.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
9.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
10.4ˣ = 64. Work out the value of x.
(a)16
(b)3
(c)4
(d)6
11.Work out √(4 × 9)
(a)5
(b)18
(c)36
(d)6
12.Given that 2⁵ = 32, work out 2⁶.
(a)34
(b)37
(c)192
(d)64
13.Work out √225 ÷ 3.
(a)8.7
(b)5
(c)75
(d)45
14.Work out ∛(−27) + ∛8
(a)5
(b)−5
(c)−1
(d)−6
15.Simplify ⁴√(16a⁸b¹²)
(a)2a²b³
(b)2a⁴b⁶
(c)4a²b³
(d)2a²b⁴

Build your own mix at the worksheet builder.