Absolutely! Let’s solve each cube root problem step by step. Since this is a
5th-grade worksheet, we’re looking for
perfect cubes — numbers that are the result of multiplying an integer by itself three times (e.g., 2 × 2 × 2 = 8).
The cube root of a number \( x \), written as \( \sqrt[3]{x} \), is the number that, when multiplied by itself three times, gives \( x \).
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Step-by-Step Solutions:
#### 1. \( \sqrt[3]{125} \)
What number cubed equals 125?
→ \( 5 × 5 × 5 = 125 \)
✔ Answer: 5
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#### 2. \( \sqrt[3]{1} \)
→ \( 1 × 1 × 1 = 1 \)
✔ Answer: 1
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#### 3. \( \sqrt[3]{4,096} \)
Let’s test some numbers:
→ \( 16 × 16 × 16 = 256 × 16 = 4,096 \)
✔ Answer: 16
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#### 4. \( \sqrt[3]{1,000} \)
→ \( 10 × 10 × 10 = 1,000 \)
✔ Answer: 10
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#### 5. \( \sqrt[3]{8} \)
→ \( 2 × 2 × 2 = 8 \)
✔ Answer: 2
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#### 6. \( \sqrt[3]{3,375} \)
Try 15: \( 15 × 15 = 225 \); \( 225 × 15 = 3,375 \)
✔ Answer: 15
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#### 7. \( \sqrt[3]{6,859} \)
Try 19: \( 19 × 19 = 361 \); \( 361 × 19 = 6,859 \)
✔ Answer: 19
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#### 8. \( \sqrt[3]{27} \)
→ \( 3 × 3 × 3 = 27 \)
✔ Answer: 3
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#### 9. \( \sqrt[3]{216} \)
→ \( 6 × 6 × 6 = 216 \)
✔ Answer: 6
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#### 10. \( \sqrt[3]{512} \)
→ \( 8 × 8 × 8 = 512 \)
✔ Answer: 8
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#### 11. \( \sqrt[3]{64} \)
→ \( 4 × 4 × 4 = 64 \)
✔ Answer: 4
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#### 12. \( \sqrt[3]{2,744} \)
Try 14: \( 14 × 14 = 196 \); \( 196 × 14 = 2,744 \)
✔ Answer: 14
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#### 13. \( \sqrt[3]{1,331} \)
→ \( 11 × 11 × 11 = 1,331 \)
✔ Answer: 11
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#### 14. \( \sqrt[3]{5,832} \)
Try 18: \( 18 × 18 = 324 \); \( 324 × 18 = 5,832 \)
✔ Answer: 18
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#### 15. \( \sqrt[3]{9,261} \)
Try 21: \( 21 × 21 = 441 \); \( 441 × 21 = 9,261 \)
✔ Answer: 21
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#### 16. \( \sqrt[3]{343} \)
→ \( 7 × 7 × 7 = 343 \)
✔ Answer: 7
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#### 17. \( \sqrt[3]{729} \)
→ \( 9 × 9 × 9 = 729 \)
✔ Answer: 9
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#### 18. \( \sqrt[3]{2,197} \)
Try 13: \( 13 × 13 = 169 \); \( 169 × 13 = 2,197 \)
✔ Answer: 13
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#### 19. \( \sqrt[3]{8,000} \)
→ \( 20 × 20 × 20 = 8,000 \)
✔ Answer: 20
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#### 20. \( \sqrt[3]{4,913} \)
Try 17: \( 17 × 17 = 289 \); \( 289 × 17 = 4,913 \)
✔ Answer: 17
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##
✔ Final Answers:
1.
5
2.
1
3.
16
4.
10
5.
2
6.
15
7.
19
8.
3
9.
6
10.
8
11.
4
12.
14
13.
11
14.
18
15.
21
16.
7
17.
9
18.
13
19.
20
20.
17
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## 💡 Tip for Students:
Memorize the first few perfect cubes to make these problems faster:
- \( 1^3 = 1 \)
- \( 2^3 = 8 \)
- \( 3^3 = 27 \)
- \( 4^3 = 64 \)
- \( 5^3 = 125 \)
- \( 6^3 = 216 \)
- \( 7^3 = 343 \)
- \( 8^3 = 512 \)
- \( 9^3 = 729 \)
- \( 10^3 = 1,000 \)
- ... and so on up to 20 or 21!
You’ve got this! 🌟
Parent Tip: Review the logic above to help your child master the concept of worksheet for 5 graders.
