Perimeter, area and volume · Ages 10–11

Square roots and cube roots worksheet

Part of: Volume

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Perimeter, area and volume · Ages 10–11

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Name:Date:Score:／48

Write each answer in the space. For word problems, show your working and write a sentence answer.

1.31 =
Answer:
2.9 =
Answer:
3.100 =
Answer:
4.A square has an area of 36 cm². How many centimetres long is each side?
Answer:
5.A square has an area of 225 cm². How many centimetres long is each side?
Answer:
6.Solid cubes are built from 1 cm cubes: 1 cm edges need 1 cube, 2 cm edges need 8 and 3 cm edges need 27. Going on like this, how many small cubes does a big cube with 10 cm edges need?
Answer:
7.45 lies between two whole numbers next to each other. What is the smaller one?
Answer:
8.124 lies between two whole numbers next to each other. What is the smaller one?
Answer:

13.A square photo has an area of 144 cm². A frame 1 cm wide goes all round it. How many centimetres long is each outer side of the frame?
Working:
Answer:
14.A square lawn has an area of 324 m². A fence goes round all four sides. How many metres long is the fence?
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Answer:
15.Chi-keung lays 225 equal square tiles to make exactly one big square. How many tiles are there along each side?
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Answer:
16.Ka-lok uses 729 cubes of 1 cm³ to build exactly one solid big cube. What is the area of one face of the big cube, in cm²?
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Answer:
17.A cube of ice has a volume of 27 cm³. How many centimetres long is each edge?
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Answer:
18.A square photo has an area of 361 cm². A frame 3 cm wide goes all round it. How many centimetres long is each outer side of the frame?
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Answer:

Show the answers and working

Square roots and cube roots worksheet: Answers and working

1. 1
Which number times itself three times makes 1? Try small numbers first and work up.
Which number times itself three times makes 1? 1 × 1 × 1 = 1, so 31 = 1.
2. 3
Which number times itself makes 9? Try small numbers first and work up.
Which number times itself makes 9? 3 × 3 = 9, so 9 = 3.
3. 10
Which number times itself makes 100? Try small numbers first and work up.
Which number times itself makes 100? 10 × 10 = 100, so 100 = 10.
4. 6 cm
Area = side × side. Which number times itself makes 36?
Area = side × side, so the side is 36 = 6: 6 × 6 = 36.
5. 15 cm
Area = side × side. Which number times itself makes 225?
Area = side × side, so the side is 225 = 15: 15 × 15 = 225.
6. 1000 cubes
1 = 1 × 1 × 1, 8 = 2 × 2 × 2, 27 = 3 × 3 × 3. How is the edge linked to the number of cubes?
1 = 1 × 1 × 1, 8 = 2 × 2 × 2, 27 = 3 × 3 × 3: 10 cm edges need 10 × 10 × 10 = 1,000.
7. 6
Find the two square numbers either side of 45: one just below it and one just above.
6 × 6 = 36 and 7 × 7 = 49; 36 < 45 < 49, so 45 is between 6 and 7.
8. 11
Find the two square numbers either side of 124: one just below it and one just above.
11 × 11 = 121 and 12 × 12 = 144; 121 < 124 < 144, so 124 is between 11 and 12.

9. False
∛ asks which number times itself three times. Try 16 × 16 × 16 and see whether it makes 64.
4 × 4 × 4 = 64, so 364 = 4.
10. C. 3 times itself makes 9
√ asks which number times itself. Think how 3 and 9 are linked.
9 asks which number times itself makes 9: 3 × 3 = 9.
11. B. 8 times itself makes 64
√ asks which number times itself. Think how 8 and 64 are linked.
64 asks which number times itself makes 64: 8 × 8 = 64.
12. True
∛ asks which number times itself three times. Try 8 × 8 × 8 and see whether it makes 512.
8 × 8 × 8 = 512, so 3512 = 8.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 14 cm
Get the photo's side from the area 144 first, then think what the frame adds at each end.
The photo's side is 144 = 12; add 1 at each end: 12 + 1 + 1 = 14.
14. 72 m
The fence is the perimeter. Get the side from the area first: which number times itself makes 324?
Side = 324 = 18 m; four sides: 4 × 18 = 72 m.
15. 15 tiles
Tiles along a side times itself gives all 225. Which number times itself makes 225?
The tiles along a side times itself is 225: 225 = 15.
16. 81 cm²
Find the big cube's edge first: which number times itself three times makes 729?
Edge = 3729 = 9 cm, so a face is 9 × 9 = 81 cm².
17. 3 cm
Edge = 327: which number times itself three times makes 27?
Edge = 327: 3 × 3 × 3 = 27, so 3 cm.
18. 25 cm
Get the photo's side from the area 361 first, then think what the frame adds at each end.
The photo's side is 361 = 19; add 3 at each end: 19 + 3 + 3 = 25.

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