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 −(−3)⁴ + (−3)³
(a)−108
(b)54
(c)−54
(d)108
2.Work out ⁴√16
(a)4
(b)8
(c)64
(d)2
3.Without using a calculator, estimate √20 × √12, giving your answer to the nearest whole number.
(a)240
(b)12
(c)8
(d)15
4.Work out 6² − 4².
(a)2
(b)52
(c)20
(d)4
5.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
6.Four students each estimate √70 without a calculator. Ben says: '8² = 64 and 9² = 81, and 70 is about a third of the way from 64 to 81, so √70 ≈ 8.3.' Chloe says: '8.5² = 72.25, which is close to 70 but a little too big, so I'll bring it down slightly to √70 ≈ 8.4.' Dan says: '9² = 81 is closer to 70 than 8² = 64 is, so √70 ≈ 8.9.' Ella says: '8² = 64 and 9² = 81, so I'll just take the midpoint of 8 and 9: √70 ≈ 8.5.' Given that √70 = 8.3666... to 4 decimal places, whose estimate is closest?
(a)Ben's estimate
(b)Chloe's estimate
(c)Ella's estimate
(d)Dan's estimate
7.4ˣ = 64. Work out the value of x.
(a)16
(b)3
(c)4
(d)6
8.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
9.Work out the exact value of √(2² + 3²)
(a)13
(b)√5
(c)5
(d)√13
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.Given that 2⁵ = 32, work out 2⁶.
(a)34
(b)37
(c)192
(d)64
12.Work out √(4 × 9)
(a)5
(b)18
(c)36
(d)6
13.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
14.Work out 5⁰ + 5¹ + 5²
(a)125
(b)30
(c)31
(d)35
15.Work out ∛(−27) + ∛8
(a)5
(b)−5
(c)−1
(d)−6

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