Numbers and operations · Ages 13–14
Square, cube and nth roots worksheet
Part of: Surds & irrational numbers
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Square, cube and nth roots worksheet
Numbers and operations · Ages 13–14
Numsprite
numsprite.com
Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.38 =
Answer:
2.256 =
Answer:
3.481 =
Answer:
4.⁵√−1024 =
Answer:
5.5184 = 2□ × 3□, so 5184 = 2□ × 3□ =
Fill in each blank
Answer:
6.4256 =
Answer:
7.324 = 2□ × 3□, so 324 = 2□ × 3□ =
Fill in each blank
Answer:
8.144 + 364 =
Answer:
Part B: Choose, or true or false (2 marks each)
9.What are the square roots of 16?
- A. −4 only
- B. 4 and −4
- C. 5 and −5
- D. 4 only
Choose the right answer
Answer:
10.256 = 16
True or false?
Answer:
11.∛−343 = 7
True or false?
Answer:
12.Which of these numbers has no square root?
- A. 20
- B. 17
- C. 0
- D. −144
Choose the right answer
Answer:
Part C: Word problems (4 marks each)
13.Someone works out 16 and gets 8. What is wrong? What is the right answer?
- (1)A square root means dividing by 2
- (2)16 ÷ 2 = 8
Find the wrong step, then write the right answer
Working:
Answer:
14.A cube has a volume of 27 cm³. How long is each edge?
Working:
Answer:
15.A cube has a volume of 343 cm³. What is its surface area, in cm²?
- A. 196
- B. 294
- C. 49
- D. 42
Choose the right answer
Working:
Answer:
16.A square carpet has an area of 324 m². Each side is m and its perimeter is m.
Fill in each blank
Working:
Answer:
17.Ka-lok says the cube root of −729 is 9. Ka-lok is right.
True or false?
Working:
Answer:
18.A cube has a surface area of 54 cm². What is its volume?
Working:
Answer:
Show the answers and working
Square, cube and nth roots worksheet: Answers and working
Part A: Working out and filling in
1. 2
(2)3 = 8, so 38 = 2. A negative number's cube root is negative.
2. 16
162 = 256, so 256 = 16 (√ means the positive square root).
3. 3
34 = 81, so the fourth root of 81 is 3. Or take the square root twice: 81 = 32, and its square root is 3.
4. −4
(−4)5 = −1024, so ⁵√−1024 = −4. An odd root keeps the number's sign.
5. 6, 4, 3, 2, 72
In primes, 5184 = 26 × 34; for the square root halve each index: 23 × 32 = 72.
6. 4
44 = 256, so the fourth root of 256 is 4. Or take the square root twice: 256 = 42, and its square root is 4.
7. 2, 4, 1, 2, 18
In primes, 324 = 22 × 34; for the square root halve each index: 21 × 32 = 18.
8. 16
144 = 12 and 364 = 4, so the sum is 16.
Part B: Choose, or true or false
9. B. 4 and −4
42 = 16 and (−4)2 = 16: both are square roots.
10. True
256 has two square roots, 16 and −16, but the sign 256 means the positive one only, 16.
11. False
(−7)3 = −343: a cube root has the number's own sign, so ∛−343 = −7.
12. D. −144
No number squared is negative, so −144 has no square root (among the real numbers).
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 4
A square root is the number whose square is 16: 42 = 16, so 16 = 4, not half of 16.
14. 3 cm
The edge cubed is 27, so the edge is 327 = 3 cm.
15. B. 294
Edge = 3343 = 7 cm, surface area = 6 × 72 = 294 cm².
16. 18, 72
Side = 324 = 18 m, perimeter = 4 × 18 = 72 m.
17. False
(−9)3 = −729, so the cube root of −729 is −9; a cube root has the number's sign.
18. 27 cm³
Each face is 54 ÷ 6 = 32, so the edge is 3 cm and the volume 33 = 27 cm³.
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