Class 8 Maths Cubes and Cube Roots Worksheet - Free Printable

Let’s solve each problem one by one, step by step.

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1. Find the cube of 15.

Cube means multiply the number by itself three times:
15 × 15 = 225
225 × 15 = ?

Break it down:
225 × 10 = 2250
225 × 5 = 1125
Add them: 2250 + 1125 = 3375

✔ Final Answer for #1: 3375

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2. Is 3087 a perfect cube?

A perfect cube is a number that can be written as n³ where n is an integer.

Let’s estimate:

14³ = 14×14=196 → 196×14 = 2744
15³ = 3375 (from above)

3087 is between 2744 and 3375 → not equal to either → so NOT a perfect cube.

We can also check prime factorization if needed, but since it’s between two consecutive cubes, it’s enough.

✔ Final Answer for #2: No

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3. If 72x is a perfect cube then x = ?

First, factor 72:

72 = 8 × 9 = 2³ × 3²

For a number to be a perfect cube, all exponents in its prime factorization must be multiples of 3.

Currently:
2³ → exponent 3 → good
3² → exponent 2 → needs one more 3 to become 3³

So we need to multiply by 3 → x = 3

Check: 72 × 3 = 216 → 6³ = 216 → yes!

✔ Final Answer for #3: 3

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4. Write ones digit of cube root of 2197.

We know 10³ = 1000, 15³ = 3375 → too big. Try 13³:

13 × 13 = 169
169 × 13 = ?

169 × 10 = 1690
169 × 3 = 507
Total = 1690 + 507 = 2197

Yes! So cube root of 2197 is 13 → ones digit is 3

✔ Final Answer for #4: 3

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5. 17 is a cube root of ________.

That means: 17³ = ?

17 × 17 = 289
289 × 17 = ?

289 × 10 = 2890
289 × 7 = 2023
Add: 2890 + 2023 = 4913

✔ Final Answer for #5: 4913

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6. The cube root of 2⁹ × 3³ × 3⁹ × 5³ is _________.

Wait — let’s rewrite the expression clearly:

It says: 2⁹ × 3³ × 3⁹ × 5³

Combine like bases:
3³ × 3⁹ = 3^(3+9) = 3¹²

So overall: 2⁹ × 3¹² × 5³

Now take cube root → divide each exponent by 3:

→ 2^(9/3) × 3^(12/3) × 5^(3/3) = 2³ × 3⁴ × 5¹

But wait — 3⁴ is not a whole power? Let me double-check the original problem.

Original: “The cube root of 2⁹ × 3³ × 3⁹ × 5³”

Actually, maybe it was meant to be 2⁹ × 3³ × 3⁹ × 5³ — which is same as 2⁹ × 3¹² × 5³

Cube root: 2³ × 3⁴ × 5¹ = 8 × 81 × 5

But 3⁴ = 81 → that’s fine, but is this simplified? Or did I misread?

Wait — perhaps the problem meant: 2⁹ × 3³ × 3⁹ × 5³ — but 3³ × 3⁹ = 3¹² → correct.

But cube root of 3¹² is 3⁴ → which is 81 → acceptable.

But let’s compute numerical value? Maybe not necessary.

Alternatively, maybe there's a typo? But assuming it’s correct:

Cube root = 2³ × 3⁴ × 5 = 8 × 81 × 5

8 × 5 = 40
40 × 81 = 3240

But actually, the question might expect the expression form? Or simplified?

Wait — looking back: “The cube root of ... is ________.” Probably expects simplified radical or number.

But 2⁹ × 3¹² × 5³ under cube root → becomes 2³ × 3⁴ × 5 = 8 × 81 × 5 = 3240

But let me verify: 3240³ should equal original? Too big.

Actually, no — cube root of A is B means B³ = A.

So if B = 2³ × 3⁴ × 5, then B³ = 2⁹ × 3¹² × 5³ → matches.

So answer is 2³ × 3⁴ × 5 = 8 × 81 × 5

Calculate: 8 × 5 = 40; 40 × 81

40 × 80 = 3200; 40 × 1 = 40 → total 3240

✔ Final Answer for #6: 3240

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7. Find the cube root of —

(i) 729

Try 9³: 9×9=81; 81×9=729 → yes → 9

(ii) 64 × 27

64 = 4³, 27 = 3³ → so product = (4×3)³ = 12³ → cube root = 12

(iii) 2744

Try 14³: 14×14=196; 196×14=2744 → yes → 14

(iv) 64000

64000 = 64 × 1000 = 4³ × 10³ = (4×10)³ = 40³ → cube root = 40

(v) 1.331

Note: 1.1³ = 1.1 × 1.1 = 1.21; 1.21 × 1.1 = 1.331 → yes → 1.1

✔ Final Answers for #7:
(i) 9
(ii) 12
(iii) 14
(iv) 40
(v) 1.1

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8. Find the cube root of 140 × 2450.

First, multiply: 140 × 2450

But better to factor first.

140 = 14 × 10 = 2×7 × 2×5 = 2² × 5 × 7
2450 = 245 × 10 = 5×49 × 2×5 = 2 × 5² × 7²

So total: 140 × 2450 = (2² × 5 × 7) × (2 × 5² × 7²) = 2³ × 5³ × 7³

Perfect cube! Cube root = 2 × 5 × 7 = 70

✔ Final Answer for #8: 70

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9. Find the smallest number by which 256 must be multiplied so that the product is a perfect cube.

Factor 256:

256 ÷ 2 = 128
128 ÷ 2 = 64
64 ÷ 2 = 32
32 ÷ 2 = 16
16 ÷ 2 = 8
8 ÷ 2 = 4
4 ÷ 2 = 2
2 ÷ 2 = 1 → so 2⁸

Exponent 8 → next multiple of 3 is 9 → need one more 2 → multiply by 2

Check: 256 × 2 = 512 = 8³ → yes!

✔ Final Answer for #9: 2

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10. If x³ = 0.008 then x = ?

0.008 = 8 / 1000 = 2³ / 10³ = (2/10)³ = (0.2)³

So x = 0.2

✔ Final Answer for #10: 0.2

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11. Find the side of the cubical box whose volume is 9261 m³.

Volume of cube = side³ → so side = cube root of 9261

Try 20³ = 8000
21³ = 21×21=441; 441×21 = ?

441×20 = 8820
441×1 = 441
Total = 8820 + 441 = 9261

Yes! Side = 21 m

✔ Final Answer for #11: 21

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12. If a³ - 1 = 1330 then a = ?

a³ = 1330 + 1 = 1331

What’s cube root of 1331?

Try 10³=1000, 11³=1331 → yes!

So a = 11

✔ Final Answer for #12: 11

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13. Find the cube root of 1331 / 1728

We know 1331 = 11³ (from above)
1728 = 12³? Check: 12×12=144; 144×12=1728 → yes!

So cube root = 11 / 12

✔ Final Answer for #13: 11/12

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14. If ∛(x/y) = 2/3 then x/y = ?

Cube both sides:

(∛(x/y))³ = (2/3)³ → x/y = 8 / 27

✔ Final Answer for #14: 8/27

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15. Three numbers are in the ratio 1 : 2 : 3 and the sum of their cubes is 288. Find the numbers.

Let the numbers be: k, 2k, 3k

Sum of cubes: k³ + (2k)³ + (3k)³ = k³ + 8k³ + 27k³ = 36k³

Set equal to 288:

36k³ = 288
k³ = 288 ÷ 36 = 8
k = ∛8 = 2

So numbers:
k = 2
2k = 4
3k = 6

Check: 2³ + 4³ + 6³ = 8 + 64 + 216 = 288 → correct!

✔ Final Answer for #15: 2, 4, 6

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Final Answer:
1. 3375
2. No
3. 3
4. 3
5. 4913
6. 3240
7. (i) 9 (ii) 12 (iii) 14 (iv) 40 (v) 1.1
8. 70
9. 2
10. 0.2
11. 21
12. 11
13. 11/12
14. 8/27
15. 2, 4, 6