FREE Printable Cube Roots Worksheets [PDFs] Brighterly - Free Printable

Let's solve the cube root problems on this worksheet step by step.

We are asked to calculate the cube root of each number, which means finding a number that, when multiplied by itself three times (cubed), gives the original number. In symbols:
If $ \sqrt[3]{x} = y $, then $ y^3 = x $.

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Let’s go through each one:

1. $ \sqrt[3]{2197} $
Try: $ 13^3 = 13 \times 13 \times 13 = 169 \times 13 = 2197 $ ✔
→ $ \boxed{13} $

2. $ \sqrt[3]{64} $
$ 4^3 = 64 $ ✔
→ $ \boxed{4} $

3. $ \sqrt[3]{8032} $
This is not a perfect cube. Let’s estimate:
$ 20^3 = 8000 $, $ 21^3 = 9261 $ → So between 20 and 21.
But since it's likely expecting exact values, maybe there's a typo? Wait — let's double-check if it's actually a perfect cube.
$ 20^3 = 8000 $, $ 20.1^3 ≈ 8120.6 $, so no. Not a perfect cube.
But wait — could it be $ \sqrt[3]{8000} $? That would be $ 20 $.
But the problem says 8032. Maybe it's not a perfect cube.
However, let’s assume only perfect cubes are intended.
But $ 8032 $ is not a perfect cube.
Let me check: $ \sqrt[3]{8032} \approx 20.02 $ — not an integer.
So perhaps it's a typo? Or we leave it as approximate?
But looking at other numbers, they seem to be perfect cubes.
Let's skip for now and come back.

4. $ \sqrt[3]{1728} $
$ 12^3 = 12 \times 12 \times 12 = 144 \times 12 = 1728 $ ✔
→ $ \boxed{12} $

5. $ \sqrt[3]{1000} $
$ 10^3 = 1000 $ ✔
→ $ \boxed{10} $

6. $ \sqrt[3]{343} $
$ 7^3 = 343 $ ✔
→ $ \boxed{7} $

7. $ \sqrt[3]{8000} $
$ 20^3 = 8000 $ ✔
→ $ \boxed{20} $

8. $ \sqrt[3]{216} $
$ 6^3 = 216 $ ✔
→ $ \boxed{6} $

9. $ \sqrt[3]{4096} $
$ 16^3 = 4096 $? Let's check:
$ 16^2 = 256 $, $ 256 \times 16 = 4096 $ ✔
→ $ \boxed{16} $

10. $ \sqrt[3]{3375} $
$ 15^3 = 15 \times 15 \times 15 = 225 \times 15 = 3375 $ ✔
→ $ \boxed{15} $

11. $ \sqrt[3]{2744} $
Try $ 14^3 = 14 \times 14 = 196 $, $ 196 \times 14 = 2744 $ ✔
→ $ \boxed{14} $

12. $ \sqrt[3]{27} $
$ 3^3 = 27 $ ✔
→ $ \boxed{3} $

13. $ \sqrt[3]{6859} $
Try $ 19^3 = 19 \times 19 = 361 $, $ 361 \times 19 = ? $
$ 361 \times 20 = 7220 $, minus $ 361 = 6859 $ ✔
→ $ \boxed{19} $

14. $ \sqrt[3]{1} $
$ 1^3 = 1 $ ✔
→ $ \boxed{1} $

15. $ \sqrt[3]{6} $
$ 6 $ is not a perfect cube. $ \sqrt[3]{6} \approx 1.817 $
But since others are integers, maybe it's a typo?
Possibly meant to be $ \sqrt[3]{8} = 2 $?
But as written, $ \sqrt[3]{6} $ is irrational.
→ $ \boxed{\sqrt[3]{6}} $ or approx $ 1.82 $ (but probably not expected)

16. $ \sqrt[3]{512} $
$ 8^3 = 512 $ ✔
→ $ \boxed{8} $

17. $ \sqrt[3]{729} $
$ 9^3 = 729 $ ✔
→ $ \boxed{9} $

18. $ \sqrt[3]{4631} $
Check nearby cubes:
$ 16^3 = 4096 $, $ 17^3 = 4913 $ → 4631 is between them.
Not a perfect cube.
$ \sqrt[3]{4631} \approx 16.66 $ → not an integer.
Probably a typo? Maybe meant $ 4096 $ or $ 4913 $?
But as is, not a perfect cube.

19. $ \sqrt[3]{125} $
$ 5^3 = 125 $ ✔
→ $ \boxed{5} $

20. $ \sqrt[3]{1331} $
$ 11^3 = 11 \times 11 = 121 $, $ 121 \times 11 = 1331 $ ✔
→ $ \boxed{11} $

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Now let's revisit the ones that aren't perfect cubes:

- $ \sqrt[3]{8032} $: $ 20^3 = 8000 $, $ 21^3 = 9261 $, so not perfect.
$ \sqrt[3]{8032} \approx 20.02 $ — very close to 20, but not exact.

- $ \sqrt[3]{6} $: Not a perfect cube.

- $ \sqrt[3]{4631} $: Between $ 16^3 = 4096 $ and $ 17^3 = 4913 $, not a perfect cube.

But given the context of a worksheet titled "Cube Roots" with clean answers, it's likely that these were intended to be perfect cubes. Perhaps typos?

Let’s recheck:

- $ \sqrt[3]{8032} $ → maybe meant $ \sqrt[3]{8000} $? Then $ \boxed{20} $
- $ \sqrt[3]{4631} $ → maybe $ \sqrt[3]{4913} = 17 $? Or $ \sqrt[3]{4096} = 16 $?
But 4631 is not a perfect cube.

Wait — what about $ \sqrt[3]{4631} $? Let’s try $ 16.6^3 $?
$ 16^3 = 4096 $, $ 17^3 = 4913 $, difference: 817
$ 4631 - 4096 = 535 $, so $ \frac{535}{817} \approx 0.655 $, so $ \approx 16.655 $
Not nice.

Similarly, $ \sqrt[3]{6} $ — clearly not a perfect cube.

So possibly the worksheet has some errors, or expects approximations.

But in most such worksheets, all values are perfect cubes.

Let’s double-check the list:

Looking again:
- $ \sqrt[3]{8032} $ — maybe typo for $ \sqrt[3]{8000} $? → 20
- $ \sqrt[3]{6} $ — maybe $ \sqrt[3]{8} $? → 2
- $ \sqrt[3]{4631} $ — maybe $ \sqrt[3]{4913} $? → 17

Alternatively, perhaps I misread.

Wait — let’s look at the image carefully.

The numbers are:

1. $ \sqrt[3]{2197} $ → 13 ✔
2. $ \sqrt[3]{64} $ → 4 ✔
3. $ \sqrt[3]{8032} $ → ???
4. $ \sqrt[3]{1728} $ → 12 ✔
5. $ \sqrt[3]{1000} $ → 10 ✔
6. $ \sqrt[3]{343} $ → 7 ✔
7. $ \sqrt[3]{8000} $ → 20 ✔
8. $ \sqrt[3]{216} $ → 6 ✔
9. $ \sqrt[3]{4096} $ → 16 ✔
10. $ \sqrt[3]{3375} $ → 15 ✔
11. $ \sqrt[3]{2744} $ → 14 ✔
12. $ \sqrt[3]{27} $ → 3 ✔
13. $ \sqrt[3]{6859} $ → 19 ✔
14. $ \sqrt[3]{1} $ → 1 ✔
15. $ \sqrt[3]{6} $ → ??
16. $ \sqrt[3]{512} $ → 8 ✔
17. $ \sqrt[3]{729} $ → 9 ✔
18. $ \sqrt[3]{4631} $ → ??
19. $ \sqrt[3]{125} $ → 5 ✔
20. $ \sqrt[3]{1331} $ → 11 ✔

So only three problematic ones: #3 ($ \sqrt[3]{8032} $), #15 ($ \sqrt[3]{6} $), #18 ($ \sqrt[3]{4631} $)

But notice: $ 8032 $ is very close to $ 8000 = 20^3 $, and $ 4631 $ is close to $ 4913 = 17^3 $, but not equal.

Perhaps it's a mistake in printing.

Alternatively, maybe $ \sqrt[3]{8032} $ is meant to be $ \sqrt[3]{8000} $? That makes sense.

And $ \sqrt[3]{6} $ — maybe it’s $ \sqrt[3]{8} $? Or $ \sqrt[3]{1} $? No.

Wait — could it be $ \sqrt[3]{64} $ already used? No.

Another idea: maybe $ \sqrt[3]{6} $ is a trick question? But unlikely.

Alternatively, perhaps the worksheet is testing estimation?

But given the style, it's more likely that the intended answers are:

| Problem | Answer |
|--------|--------|
| $ \sqrt[3]{2197} $ | 13 |
| $ \sqrt[3]{64} $ | 4 |
| $ \sqrt[3]{8032} $ | Probably typo; should be 8000 → 20 |
| $ \sqrt[3]{1728} $ | 12 |
| $ \sqrt[3]{1000} $ | 10 |
| $ \sqrt[3]{343} $ | 7 |
| $ \sqrt[3]{8000} $ | 20 |
| $ \sqrt[3]{216} $ | 6 |
| $ \sqrt[3]{4096} $ | 16 |
| $ \sqrt[3]{3375} $ | 15 |
| $ \sqrt[3]{2744} $ | 14 |
| $ \sqrt[3]{27} $ | 3 |
| $ \sqrt[3]{6859} $ | 19 |
| $ \sqrt[3]{1} $ | 1 |
| $ \sqrt[3]{512} $ | 8 |
| $ \sqrt[3]{729} $ | 9 |
| $ \sqrt[3]{4631} $ | Probably typo; should be 4913 → 17 |
| $ \sqrt[3]{125} $ | 5 |
| $ \sqrt[3]{1331} $ | 11 |

But $ \sqrt[3]{6} $ remains odd.

Wait — perhaps it's $ \sqrt[3]{8} $? But it says 6.

Alternatively, maybe it's $ \sqrt[3]{6} $ as a radical expression? But the others are integers.

Alternatively, could it be $ \sqrt[3]{64} $? Already listed.

Wait — maybe the worksheet is from a source where some values are not perfect cubes, and we're supposed to estimate.

But given the title "Geometry Worksheet", and the way it's formatted, it's likely only perfect cubes are intended.

Let’s check if $ \sqrt[3]{8032} $ might be a typo for $ \sqrt[3]{8000} $? Yes, plausible.

Similarly, $ \sqrt[3]{4631} $ — maybe $ \sqrt[3]{4913} $? 17³ = 4913, yes.

But 4631 ≠ 4913.

Wait — what is $ 16.6^3 $?
$ 16^3 = 4096 $, $ 17^3 = 4913 $, $ 16.5^3 = ? $
$ 16.5^2 = 272.25 $, $ 272.25 \times 16.5 = ? $
$ 272.25 \times 16 = 4356 $, $ 272.25 \times 0.5 = 136.125 $, total = 4492.125
Still less than 4631.

$ 16.7^2 = 278.89 $, $ 278.89 \times 16.7 \approx ? $
$ 278.89 \times 16 = 4462.24 $, $ 278.89 \times 0.7 = 195.223 $, total ≈ 4657.46 — too high.

So $ \sqrt[3]{4631} \approx 16.65 $

Not nice.

So best guess: the worksheet may have typos.

But for now, assuming the intent was perfect cubes, here are the answers:

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Final Answers (assuming perfect cubes):

1. $ \sqrt[3]{2197} = \boxed{13} $
2. $ \sqrt[3]{64} = \boxed{4} $
3. $ \sqrt[3]{8032} = \boxed{20} $ *(likely typo for 8000)*
4. $ \sqrt[3]{1728} = \boxed{12} $
5. $ \sqrt[3]{1000} = \boxed{10} $
6. $ \sqrt[3]{343} = \boxed{7} $
7. $ \sqrt[3]{8000} = \boxed{20} $
8. $ \sqrt[3]{216} = \boxed{6} $
9. $ \sqrt[3]{4096} = \boxed{16} $
10. $ \sqrt[3]{3375} = \boxed{15} $
11. $ \sqrt[3]{2744} = \boxed{14} $
12. $ \sqrt[3]{27} = \boxed{3} $
13. $ \sqrt[3]{6859} = \boxed{19} $
14. $ \sqrt[3]{1} = \boxed{1} $
15. $ \sqrt[3]{6} = \boxed{\sqrt[3]{6}} $ or approx $ \boxed{1.82} $ *(not perfect cube)*
16. $ \sqrt[3]{512} = \boxed{8} $
17. $ \sqrt[3]{729} = \boxed{9} $
18. $ \sqrt[3]{4631} = \boxed{17} $ *(if typo for 4913)* or $ \boxed{\sqrt[3]{4631}} $
19. $ \sqrt[3]{125} = \boxed{5} $
20. $ \sqrt[3]{1331} = \boxed{11} $

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Recommendation:

Check for possible typos in the original worksheet:
- $ \sqrt[3]{8032} $ → likely $ \sqrt[3]{8000} $
- $ \sqrt[3]{4631} $ → likely $ \sqrt[3]{4913} $
- $ \sqrt[3]{6} $ → possibly $ \sqrt[3]{8} $ or $ \sqrt[3]{1} $

But based on the image as is, here are the correct values:

✔ Perfect Cube Answers:

| Expression | Answer |
|----------|--------|
| $ \sqrt[3]{2197} $ | 13 |
| $ \sqrt[3]{64} $ | 4 |
| $ \sqrt[3]{1728} $ | 12 |
| $ \sqrt[3]{1000} $ | 10 |
| $ \sqrt[3]{343} $ | 7 |
| $ \sqrt[3]{8000} $ | 20 |
| $ \sqrt[3]{216} $ | 6 |
| $ \sqrt[3]{4096} $ | 16 |
| $ \sqrt[3]{3375} $ | 15 |
| $ \sqrt[3]{2744} $ | 14 |
| $ \sqrt[3]{27} $ | 3 |
| $ \sqrt[3]{6859} $ | 19 |
| $ \sqrt[3]{1} $ | 1 |
| $ \sqrt[3]{512} $ | 8 |
| $ \sqrt[3]{729} $ | 9 |
| $ \sqrt[3]{125} $ | 5 |
| $ \sqrt[3]{1331} $ | 11 |

For non-perfect cubes:
- $ \sqrt[3]{8032} \approx 20.02 $
- $ \sqrt[3]{6} \approx 1.817 $
- $ \sqrt[3]{4631} \approx 16.65 $

But since this is likely a learning exercise, the intended answers are probably the perfect cube roots, and the others may be typos.

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✔ Final Answer Key (assuming perfect cubes):

1. 13
2. 4
3. 20 *(assumed typo)*
4. 12
5. 10
6. 7
7. 20
8. 6
9. 16
10. 15
11. 14
12. 3
13. 19
14. 1
15. $ \sqrt[3]{6} $ or 1.82
16. 8
17. 9
18. 17 *(assumed typo)*
19. 5
20. 11

But if you must fill in the blanks as per the image:

Best guesses:
- $ \sqrt[3]{8032} \to \boxed{20} $
- $ \sqrt[3]{6} \to \boxed{\sqrt[3]{6}} $
- $ \sqrt[3]{4631} \to \boxed{17} $ *(if typo)*

But strictly speaking, without confirmation, we can only give exact values for perfect cubes.

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✔ Correct Answers (only perfect cubes):

$$
\begin{aligned}
&\sqrt[3]{2197} = 13 \\
&\sqrt[3]{64} = 4 \\
&\sqrt[3]{1728} = 12 \\
&\sqrt[3]{1000} = 10 \\
&\sqrt[3]{343} = 7 \\
&\sqrt[3]{8000} = 20 \\
&\sqrt[3]{216} = 6 \\
&\sqrt[3]{4096} = 16 \\
&\sqrt[3]{3375} = 15 \\
&\sqrt[3]{2744} = 14 \\
&\sqrt[3]{27} = 3 \\
&\sqrt[3]{6859} = 19 \\
&\sqrt[3]{1} = 1 \\
&\sqrt[3]{512} = 8 \\
&\sqrt[3]{729} = 9 \\
&\sqrt[3]{125} = 5 \\
&\sqrt[3]{1331} = 11 \\
\end{aligned}
$$

For the rest:
- $ \sqrt[3]{8032} $: Not a perfect cube → $ \approx 20.02 $
- $ \sqrt[3]{6} $: $ \approx 1.82 $
- $ \sqrt[3]{4631} $: $ \approx 16.65 $

But in the context of this worksheet, likely intended answers are:

> Final Answer Boxed (as per likely intent):

$$
\boxed{
\begin{array}{c|c}
\text{Expression} & \text{Answer} \\
\hline
\sqrt[3]{2197} & 13 \\
\sqrt[3]{64} & 4 \\
\sqrt[3]{8032} & 20 \\
\sqrt[3]{1728} & 12 \\
\sqrt[3]{1000} & 10 \\
\sqrt[3]{343} & 7 \\
\sqrt[3]{8000} & 20 \\
\sqrt[3]{216} & 6 \\
\sqrt[3]{4096} & 16 \\
\sqrt[3]{3375} & 15 \\
\sqrt[3]{2744} & 14 \\
\sqrt[3]{27} & 3 \\
\sqrt[3]{6859} & 19 \\
\sqrt[3]{1} & 1 \\
\sqrt[3]{6} & \sqrt[3]{6} \\
\sqrt[3]{512} & 8 \\
\sqrt[3]{729} & 9 \\
\sqrt[3]{4631} & 17 \\
\sqrt[3]{125} & 5 \\
\sqrt[3]{1331} & 11 \\
\end{array}
}
$$

With notes: $ \sqrt[3]{8032} $ and $ \sqrt[3]{4631} $ likely contain typos. $ \sqrt[3]{6} $ is irrational.

But for practical purposes, fill in the blanks with the perfect cube values, and assume the others are mistakes.

✔ Conclusion: The cube roots of the perfect cubes are integers as shown above. For non-perfect cubes, either accept approximation or suspect typo.