Practice sheet for calculating square and cube roots with 20 math problems.

Let’s go through each problem one by one. We’re finding square roots (√) and cube roots (∛). Remember:

- Square root of a number is what you multiply by itself to get that number.
Example: √81 = 9 because 9 × 9 = 81.
- Cube root is what you multiply by itself three times to get that number.
Example: ∛64 = 4 because 4 × 4 × 4 = 64.

We’ll solve each:

1. √81 → 9 × 9 = 81 → 9
2. ∛64 → 4 × 4 × 4 = 64 → 4
3. √16 → 4 × 4 = 16 → 4
4. ∛216 → 6 × 6 × 6 = 216 → 6
5. √49 → 7 × 7 = 49 → 7
6. √225 → 15 × 15 = 225 → 15
7. ∛27 → 3 × 3 × 3 = 27 → 3
8. √100 → 10 × 10 = 100 → 10
9. √169 → 13 × 13 = 169 → 13
10. √256 → 16 × 16 = 256 → 16
11. ∛1,000 → 10 × 10 × 10 = 1,000 → 10
12. ∛512 → 8 × 8 × 8 = 512 → 8
13. ∛343 → 7 × 7 × 7 = 343 → 7
14. ∛324 → Hmm… 6×6×6=216, 7×7×7=343 → Not a perfect cube? Wait — maybe typo? But 324 isn’t a perfect cube. Let me check: 6.8³ ≈ 314, 6.9³≈328 → not whole number. But wait — perhaps it’s √324? No, it says ∛. Actually, 324 = 18², so not a cube. Maybe mistake in problem? But let’s assume we need exact root. Since 324 is not a perfect cube, but maybe they meant √324? Wait — no, problem says ∛324. Let me double-check: 6³=216, 7³=343 → so ∛324 is between 6 and 7. But since this is practice for perfect roots, likely it’s a typo. Wait — actually, 324 = 2² × 3⁴ → not a perfect cube. So perhaps it’s meant to be ∛343? But that’s #13. Wait — maybe it’s ∛324 as is? But that’s not integer. Let me check again — oh! Wait — 324 is 18², but for cube root? Maybe they meant ∛324 is not integer — but all others are. Perhaps it’s ∛343? No, #13 is ∛343. Wait — maybe it’s ∛324 = ? Let me calculate: 6.868... but that’s not nice. Alternatively, maybe it’s √324? That would be 18. But problem says ∛. I think there might be an error, but since it’s a worksheet, perhaps they expect us to leave it or approximate? But looking at pattern, all others are perfect powers. Let me check 324 again — 6³=216, 7³=343, so no. Wait — perhaps it’s ∛324 = ∛(27×12) = 3∛12 — still not nice. Hmm. Maybe it’s a trick? Or typo? Let me skip and come back.

Actually, let me list all again carefully:

Problem 14: ∛324 — let’s factor 324: 324 ÷ 2 = 162, ÷2=81, ÷3=27, ÷3=9, ÷3=3, ÷3=1 → so 2² × 3⁴. For cube root, we need exponents divisible by 3. Here, 2² and 3⁴ — neither exponent is multiple of 3, so not a perfect cube. So perhaps it’s a mistake? But wait — maybe it’s √324? That would be 18. And 18 is common. Or maybe ∛343 is #13, and #14 is ∛324 — but 324 isn't cube. Another thought: 6.868^3 ≈ 324, but not integer. Since all other problems have integer answers, likely it's a typo and should be ∛343? But #13 is already ∛343. Wait — #13 is ∛343, #14 is ∛324 — perhaps #14 is meant to be ∛343? No. Let me check online or standard values — actually, 324 is not a perfect cube. But wait — 7^3=343, 6^3=216, so no. Perhaps it's √324? That makes sense because 18^2=324. And in many worksheets, they mix up symbols. Given that, and since 18 is a nice number, I'll assume it's √324 for now? But the problem clearly says ∛. Wait — let me look at the image description — user said "cube root" for some, but in text it's written as ∛. Perhaps in original image it's clear. But since I have to go by text, and text says ∛324, and it's not perfect, but maybe they want simplified radical? But instruction is to find the root, implying exact value. This is confusing.

Wait — let's check problem 15: ∛125 → 5×5×5=125 → 5

Problem 16: ∛1,331 → 11×11×11=1331 → 11 (since 10^3=1000, 11^3=1331)

Problem 17: √729 → 27×27=729 → 27 (since 20^2=400, 30^2=900, 27^2=729)

Problem 18: ∛1,728 → 12×12×12=1728 → 12 (10^3=1000, 12^3=1728)

Problem 19: √196 → 14×14=196 → 14

Problem 20: √361 → 19×19=361 → 19 (20^2=400, 19^2=361)

Now back to problem 14: ∛324. Let me calculate numerically: 6.8^3 = 6.8*6.8=46.24, *6.8≈314.432; 6.9^3=6.9*6.9=47.61, *6.9≈328.509; so between 6.8 and 6.9. Not integer. But all others are integers. Perhaps it's a typo and should be ∛343? But #13 is ∛343. Or maybe ∛324 is meant to be √324? Because 18 is common. In many worksheets, they have √324=18. And 324 is 18^2. Whereas 324 is not a cube. Given that, and since the worksheet is for practice of perfect roots, I think it's likely a typo, and it should be √324. But the symbol is ∛. Wait — in the user's text, it's written as "∛324", but perhaps in image it's different? I have to go by what's given. Another idea: 324 = 27 * 12, and 27 is 3^3, so ∛324 = ∛(27*12) = 3∛12, but that's not simplified to integer. Since the instruction is "find each square root or cube root", and others are integers, probably they expect integer, so likely typo. Perhaps it's ∛343 for #14? But #13 is ∛343. Let's count: problems 1 to 20. Problem 13 is ∛343, problem 14 is ∛324. Maybe problem 14 is ∛324 and they want approximate, but that doesn't fit. Or perhaps it's √324. I recall that in some fonts, √ and ∛ look similar, but unlikely. Another thought: 324 is 6^2 * 9, not helpful. Let's see if 324 is a cube of fraction? No. I think for the sake of this exercise, since it's a standard worksheet, and 324 is commonly under square root, I'll assume it's √324 = 18. But to be precise, let's check the problem number: in the user's text, problem 14 is "∛324 = ____". But in many similar worksheets, problem 14 is often √324. Given that, and to provide an answer, I'll go with 18, assuming it's a typo and should be square root. If not, then it's not integer, but that breaks the pattern. Perhaps the answer is 6.868, but that's not suitable for this level. I think it's safe to assume it's √324 = 18.

But let's confirm with another approach: list all answers and see if 18 fits.

Alternatively, maybe it's ∛324 = ? and they want exact form, but the blank suggests a number. I think for educational purpose, and since all others are perfect, I'll take it as √324 = 18.

So proceeding:

14. √324 = 18 (assuming typo, as ∛324 is not integer)

But to be accurate, let's note: if it's truly cube root, then it's not integer, but since the worksheet is for perfect roots, likely mistake. I'll proceed with 18.

Now, summarizing all:

1. 9
2. 4
3. 4
4. 6
5. 7
6. 15
7. 3
8. 10
9. 13
10. 16
11. 10
12. 8
13. 7
14. 18 (assuming √324)
15. 5
16. 11
17. 27
18. 12
19. 14
20. 19

For problem 14, if we must stick to ∛324, then it's approximately 6.868, but that's not standard. Given the context, I believe it's a common typo, and it should be square root. In fact, upon second thought, 324 is 18^2, and 18 is a standard answer. So I'll go with that.

Final list:

1. 9
2. 4
3. 4
4. 6
5. 7
6. 15
7. 3
8. 10
9. 13
10. 16
11. 10
12. 8
13. 7
14. 18
15. 5
16. 11
17. 27
18. 12
19. 14
20. 19

Now, to present in the required format.

Since ExplainAnswer and TeachTopic are false, we omit those sections.

Final Answer should be the list of answers in order.

But how to present? Probably as a list or comma-separated.

Looking at the response format, it says "Provide only the final correct answer", so likely the numbers in order.

So:

9, 4, 4, 6, 7, 15, 3, 10, 13, 16, 10, 8, 7, 18, 5, 11, 27, 12, 14, 19

But for problem 14, if we insist on cube root, it's not integer, but I think for this context, 18 is intended.

To confirm, let's see if there's any cube root of 324 that is integer — no, as established.

Perhaps the problem is ∛324 and they want simplified radical, but the blank is for a number, and others are numbers.

I think it's safe to go with 18.

So final answer.