IGCSE · Mathematics 0580 · Number

Powers & roots: IGCSE Mathematics questions with answers

Free Powers & roots questions for IGCSE Mathematics (0580), part of Number. Each question has the answer and the marking points an examiner would look for.

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Powers & roots practice questions

Question 1Structured · 3 marksA* challenge

Find the value of

(a)

6423

[2]
(b)

(16)−12

[1]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)16
∛64 = 4 M1
16 A1
2
(b)14
14 B1
1
Question 2Structured · 4 marks

Work out

(a)

33

[1]
(b)

∛216

[1]
(c)

√144 − 20

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)27
27 B1
1
(b)6
6 B1
1
(c)11
√144 = 12 or 20 = 1 M1
11 A1
2
Question 3Structured · 4 marks
(a)

Work out 32.

[1]
(b)

Write down the value of √225.

[1]
(c)

Write down the value of ∛216.

[1]
(d)

Find the value of 4−2.

[1]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)9
9 B1
1
(b)15
15 B1
1
(c)6
6 B1
1
(d)116
116 B1
1
Question 4Structured · 3 marks
(a)

Write 784 as a product of its prime factors in index form.

[2]
(b)

Hence find √784.

[1]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)24 × 72
method M1
24 × 72 A1
2
(b)28
28 B1
1
Question 5Structured · 3 marksA* challenge

Find the value of

(a)

823

[2]
(b)

(4)−12

[1]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)4
∛8 = 2 M1
4 A1
2
(b)12
12 B1
1
Question 6Structured · 4 marks

Work out

(a)

54

[1]
(b)

∛125

[1]
(c)

√144 − 20

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)625
625 B1
1
(b)5
5 B1
1
(c)11
√144 = 12 or 20 = 1 M1
11 A1
2

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Original Cambridge-style practice questions written for mentorriyaz.in. These are not Cambridge past paper questions, and this site is not affiliated with or endorsed by Cambridge University Press & Assessment. Updated 2026-11-04. Paper generator · mentorriyaz.in