Chapter-wise Worksheets for Class 8 Mathematics: Chapter 07 Cubes and Cube Roots
Review targeted academic worksheets with the CBSE Class 8 Mathematics Cubes and Cube Roots Practice Paper Worksheet Set 06 with Answers (Old NCERT Syllabus). Built according to official educational standards for the 2026-27 term, these downloadable Class 8 Mathematics resources support effective daily practice and detailed self-evaluation for Chapter 07 Cubes and Cube Roots.
Practice Class 8 Mathematics Worksheets: Chapter 07 Cubes and Cube Roots
Access the complete worksheet PDF for Class 8 Mathematics below. Regular practice with these targeted academic tasks builds familiarity with standard question patterns and helps secure higher marks in final school examinations.
This Class 8 Maths Cubes and Cube Roots practice paper carries 40 marks and has 17 questions in five sections: six MCQs including an Assertion–Reason item, short and long answer questions and a case study, all with step-by-step answers. It follows the earlier (old) NCERT Class 8 Maths syllabus, which makes it handy for state-board students and for revising this chapter. The paper tests cube roots by prime factorisation, cube roots of decimals and fractions, the smallest multiplier or divisor that gives a perfect cube, and building cubes from identical cuboids.
Section A: Multiple Choice Questions (1 Mark Each)
(a) 2
(b) 3
(c) 6
(d) 7
Show Answer & Explanation
Answer: (a) 2
Explanation:
1. Start inside: 343 = 7 × 7 × 7, so \( \sqrt[3]{343} \) = 7.
2. Then the expression = \( \sqrt[3]{1 + 7} \) = \( \sqrt[3]{8} \).
3. 8 = 2 × 2 × 2, so \( \sqrt[3]{8} \) = 2.
4. So the value is 2.
Teacher's Note:
1. Work from the innermost root outwards.
2. 7 is the trap: it is only the inner root, not the final answer.
(a) 3
(b) 5
(c) 40
(d) 125
Show Answer & Explanation
Answer: (b) 5
Explanation:
1. 675 = 3 × 3 × 3 × 5 × 5.
2. 3 already forms a triplet; 5 appears only twice.
3. One more 5 completes the triplet: 675 × 5 = 3375 = 15³.
4. So the smallest multiplier is 5.
Teacher's Note:
1. Group the prime factors in threes; multiply by whatever completes each incomplete group.
2. 125 would also give a cube, but it is not the smallest.
(a) 216
(b) 567
(c) 125
(d) 343
Show Answer & Explanation
Answer: (b) 567
Explanation:
1. 216 = 6³, 125 = 5³ and 343 = 7³ are all perfect cubes.
2. 567 = 3 × 3 × 3 × 3 × 7 = 3³ × 3 × 7.
3. The factors 3 (one extra) and 7 are not in triplets, so 567 is not a perfect cube.
4. So the answer is 567.
Teacher's Note:
1. Know the cubes 1³ to 10³: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000.
2. 567 lies between 8³ = 512 and 9³ = 729, so it cannot be a cube.
(a) 6.327
(b) 63.275
(c) 632.75
(d) 62.757
Show Answer & Explanation
Answer: (d) 62.757
Explanation:
1. 185.193 = \( \frac{185193}{1000} \), so \( \sqrt[3]{185.193} \) = \( \frac{57}{10} \) = 5.7 (since 10³ = 1000).
2. 0.000185193 = \( \frac{185193}{10^9} \), so \( \sqrt[3]{0.000185193} \) = \( \frac{57}{1000} \) = 0.057 (since 1000³ = 10⁹).
3. Sum = 57 + 5.7 + 0.057 = 62.757.
4. So the value is 62.757.
Teacher's Note:
1. The cube root of a decimal has one-third as many decimal places: 3 places → 1 place, 9 places → 3 places.
2. Check: 5.7³ = 185.193.
(a) 2
(b) 3
(c) 4
(d) 9
Show Answer & Explanation
Answer: (b) 3
Explanation:
1. \( \sqrt[3]{64} \) = 4, \( \sqrt[3]{125} \) = 5 and \( \sqrt[3]{27} \) = 3.
2. Value = \( \frac{4 + 5}{3} \) = \( \frac{9}{3} \) = 3.
3. So the value is 3.
Teacher's Note:
1. Find each cube root separately; you cannot add the numbers under the roots.
2. 9 is the trap: it is only the numerator.
Assertion (A): The one’s digit in the cube root of the cube number 1728 is 6.
Reason (R): The cube root of a number is the factor that we multiply by itself three times to get that number.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation
Answer: (d) A is false, but R is true.
Explanation:
1. 1728 = 12 × 12 × 12, so \( \sqrt[3]{1728} \) = 12, whose one’s digit is 2.
2. Quick rule: a cube ending in 8 has a cube root ending in 2 (2³ = 8). So A is false.
3. R is the correct meaning of a cube root. So R is true.
4. So the answer is (d) A is false but R is true.
Teacher's Note:
1. Units digit pairs for cubes: 2 ↔ 8 and 3 ↔ 7; the digits 0, 1, 4, 5, 6, 9 stay the same.
2. 6³ = 216 ends in 6, not 8, so 6 cannot be the answer.
Section B: Short Answer Questions (2 Marks Each)
Question 7. Find the length of each side of a cube if its volume is 512 cm3.
Answer:
Volume of a cube = side³, so side³ = 512.
512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) = 8 × 8 × 8.
So side = \( \sqrt[3]{512} \) = 8.
Length of each side = 8 cm.
In simple words: The side of a cube is the cube root of its volume, and 8 × 8 × 8 = 512.
Teacher's Note:
1. Group the prime factors in threes and take one factor from each group.
2. Do not divide 512 by 3; that gives nothing useful.
Question 8. What is the smallest number by which 1323 may be multiplied so that the product is a perfect cube?
Answer:
Prime factorisation: 1323 = 3 × 3 × 3 × 7 × 7.
3 forms a triplet (3 × 3 × 3), but 7 occurs only twice.
One more 7 is needed to complete the triplet of 7.
1323 × 7 = 9261 = 21³.
Smallest number to multiply by = 7.
In simple words: 1323 = 3³ × 7², so it needs just one more 7 to become 21³ = 9261.
Teacher's Note:
1. Divide by small primes in order: 1323 ÷ 3 = 441, 441 ÷ 3 = 147, 147 ÷ 3 = 49, 49 = 7 × 7.
2. Check by computing the cube root of the product: 3 × 7 = 21.
Question 9. What is the smallest number by which 1375 should be divided so that the quotient may be a perfect cube?
Answer:
Prime factorisation: 1375 = 5 × 5 × 5 × 11.
5 forms a triplet, but 11 occurs only once and is left over.
Divide by 11 to remove it: 1375 ÷ 11 = 125 = 5³.
Smallest number to divide by = 11.
In simple words: 1375 is 5³ × 11, so dividing by 11 leaves the perfect cube 125.
Teacher's Note:
1. When dividing, remove the factors that are not in complete triplets.
2. When multiplying, add factors to complete the triplets instead.
Section C: Short Answer Questions (3 Marks Each)
Question 10. Sujatha makes a cuboid of plasticine of sides 5 cm, 2 cm, 5 cm. How many minimum such cuboids will she need to form a cube?
Answer:
Volume of one cuboid = 5 × 2 × 5 = 50 cm³ = 2 × 5 × 5.
For a perfect cube every prime factor must occur in triplets.
5 occurs twice (needs one more 5) and 2 occurs once (needs 2 × 2).
So the volume must be multiplied by 5 × 2 × 2 = 20.
20 cuboids give 50 × 20 = 1000 cm³ = 10³, a cube of side 10 cm (2 cuboids along each 5 cm edge and 5 along the 2 cm edge: 2 × 2 × 5 = 20).
Minimum number of cuboids = 20.
In simple words: One cuboid has volume 50 = 2 × 5²; multiplying by 20 makes 1000 = 10³, so 20 cuboids form a 10 cm cube.
Teacher's Note:
1. The number of cuboids is the smallest multiplier that makes the volume a perfect cube.
2. Check that the cuboids actually fit: 10 ÷ 5 = 2, 10 ÷ 2 = 5, 10 ÷ 5 = 2, and 2 × 5 × 2 = 20.
Question 11. Evaluate: \( \sqrt[3]{27} + \sqrt[3]{0.008} + \sqrt[3]{0.064} \)
Answer:
\( \sqrt[3]{27} \) = \( \sqrt[3]{3 \times 3 \times 3} \) = 3.
\( \sqrt[3]{0.008} \) = \( \sqrt[3]{0.2 \times 0.2 \times 0.2} \) = 0.2 (as 2³ = 8 and 0.008 has 3 decimal places).
\( \sqrt[3]{0.064} \) = \( \sqrt[3]{0.4 \times 0.4 \times 0.4} \) = 0.4 (as 4³ = 64).
Sum = 3 + 0.2 + 0.4 = 3.6.
In simple words: The three cube roots are 3, 0.2 and 0.4, which add up to 3.6.
Teacher's Note:
1. A decimal with 3 decimal places has a cube root with 1 decimal place.
2. Check: 0.2³ = 0.008 and 0.4³ = 0.064.
Question 12. Find the cube root of \( 4\frac{12}{125} \)
Answer:
Convert to an improper fraction: \( 4\frac{12}{125} = \frac{4 \times 125 + 12}{125} = \frac{512}{125} \).
512 = 8 × 8 × 8 = 8³ and 125 = 5 × 5 × 5 = 5³.
\( \sqrt[3]{\frac{512}{125}} = \frac{\sqrt[3]{512}}{\sqrt[3]{125}} = \frac{8}{5} \).
Cube root = \( \frac{8}{5} \) = \( 1\frac{3}{5} \) = 1.6.
In simple words: 4 12/125 is 512/125, and the cube roots of 512 and 125 are 8 and 5, giving 8/5.
Teacher's Note:
1. Always change a mixed number to an improper fraction before taking a root.
2. Check: (8/5)³ = 512/125 = 4 12/125.
Question 13. By what smallest number should 3600 be multiplied so that the product is a perfect cube. Also, find the cube root of the product.
Answer:
Prime factorisation: 3600 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5.
Grouping in triplets: (2 × 2 × 2) × 2 × (3 × 3) × (5 × 5).
To complete the triplets we need 2 × 2 (for the extra 2), one 3 and one 5.
Smallest multiplier = 2 × 2 × 3 × 5 = 60.
Product = 3600 × 60 = 216000 = (2 × 2 × 2) × (2 × 2 × 2) × (3 × 3 × 3) × (5 × 5 × 5).
Cube root of the product = 2 × 2 × 3 × 5 = 60.
In simple words: 3600 = 2⁴ × 3² × 5² needs 2² × 3 × 5 = 60 more, and 3600 × 60 = 216000 = 60³.
Teacher's Note:
1. Count each prime's power and raise it to the next multiple of 3: 2⁴ → 2⁶, 3² → 3³, 5² → 5³.
2. The word in the paper was "quotient"; with multiplication the result is a product.
Section D: Long Answer Questions (4 Marks Each)
Question 14. Find the smallest number which when multiplied with 3600 will make the product a perfect cube. Find the cube root of the product.
Answer:
Prime factorisation: 3600 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5.
Grouping in triplets: (2 × 2 × 2) × 2 × (3 × 3) × (5 × 5).
To complete the triplets we need 2 × 2 (for the extra 2), one 3 and one 5.
Smallest multiplier = 2 × 2 × 3 × 5 = 60.
Product = 3600 × 60 = 216000 = (2 × 2 × 2) × (2 × 2 × 2) × (3 × 3 × 3) × (5 × 5 × 5).
Cube root of the product = 2 × 2 × 3 × 5 = 60.
In simple words: 3600 = 2⁴ × 3² × 5² needs 2² × 3 × 5 = 60 more, and 3600 × 60 = 216000 = 60³.
Teacher's Note:
1. Count each prime's power and raise it to the next multiple of 3.
2. Here 2⁴ → 2⁶, 3² → 3³ and 5² → 5³.
Question 15. Find the value of \( \sqrt[3]{968} \times \sqrt[3]{1375} \)
OR
Three numbers are in the ratio 1 : 2 : 3 and the sum of their cubes is 4500. Find the numbers.
Answer:
\( \sqrt[3]{968} \times \sqrt[3]{1375} = \sqrt[3]{968 \times 1375} \).
968 = 2 × 2 × 2 × 11 × 11 and 1375 = 5 × 5 × 5 × 11.
968 × 1375 = (2 × 2 × 2) × (11 × 11 × 11) × (5 × 5 × 5).
Cube root = 2 × 11 × 5 = 110.
OR
Let the numbers be x, 2x and 3x.
x³ + (2x)³ + (3x)³ = 4500, so x³ + 8x³ + 27x³ = 4500.
36x³ = 4500, so x³ = 4500 ÷ 36 = 125.
x = \( \sqrt[3]{125} \) = 5.
The numbers are 5, 10 and 15.
Check: 125 + 1000 + 3375 = 4500.
In simple words: 968 × 1375 = 2³ × 5³ × 11³, so the value is 110; in the OR question 36x³ = 4500 gives x = 5 and the numbers 5, 10, 15.
Teacher's Note:
1. The product of cube roots is the cube root of the product.
2. (2x)³ = 8x³, not 2x³: cube the number and the variable.
Question 16. Find the smallest number by which 33275 must be divided so that the quotient has a cube root. Also, find the cube root of the quotient.
Answer:
Prime factorisation: 33275 = 5 × 5 × 11 × 11 × 11.
Grouping: 5 × 5 × (11 × 11 × 11); 11 forms a triplet but 5 occurs only twice.
Remove the unpaired factors: divide by 5 × 5 = 25.
Quotient = 33275 ÷ 25 = 1331 = 11 × 11 × 11.
Cube root of the quotient = 11.
In simple words: 33275 = 5² × 11³; dividing by 25 leaves 1331 = 11³.
Teacher's Note:
1. 33275 ends in 5, so start dividing by 5.
2. "Has a cube root" here means "is a perfect cube".
Section E: Case Study Based Question (4 Marks)
Question 17. Mohan has to prepare a physics project in form of a cubical box for a social work campaign but he had a cuboidal box of sides 4 cm, 2 cm, 4 cm. Now he has to change it in the form of cube so that he can complete his project. For this, he needed more cuboids so that he can make his project in form of cube.
(a) What is the volume of the cuboidal box? [1]
(b) Find value of (0.02)3. [1]
(c) How many cuboids are more needed? [2]
Answer:
(a) Volume of the cuboid = l × b × h = 4 × 2 × 4 = 32 cm³.
(b) \( (0.02)^3 = \frac{2}{100} \times \frac{2}{100} \times \frac{2}{100} = \frac{8}{1000000} \) = 0.000008.
(c) 32 = 2 × 2 × 2 × 2 × 2 = 2⁵. For a perfect cube the power of 2 must be a multiple of 3, so we need 2⁶ = 64.
So the volume must be doubled: 32 × 2 = 64 cm³ = 4³, a cube of side 4 cm.
Two cuboids of 4 cm × 4 cm × 2 cm placed one on top of the other (2 cm + 2 cm = 4 cm) make a 4 cm × 4 cm × 4 cm cube.
Mohan already has 1 cuboid, so he needs 1 more cuboid (2 cuboids in all).
In simple words: Two 4 × 4 × 2 boxes stacked make a 4 cm cube, so Mohan needs just one more box.
Teacher's Note:
1. Find the smallest multiplier that makes the volume a perfect cube; that is the number of cuboids.
2. Always check that the cuboids really fit together: two 2 cm heights make 4 cm.
Free study material for Mathematics
CBSE Class 8 Mathematics Worksheets for Chapter 07 Cubes and Cube Roots
Daily Practice Questions for Class 8 Mathematics
Explore reliable practice questions for Chapter 07 Cubes and Cube Roots tailored for Class 8 Mathematics learners. Use these structured worksheets to evaluate exam preparedness and strengthen problem-solving skills throughout the 2026 academic session.
Detailed Answers for Class 8 Mathematics Chapter 07 Cubes and Cube Roots
Each worksheet draws directly from authorized standard textbooks to maintain academic accuracy. Evaluating your finished exercises against expert-verified solutions helps master the formal presentation standards expected in school evaluations.
Complete Your Chapter Revision
Wrap up your chapter revision by testing your knowledge against standard objective question formats. Explore our full library of free, up-to-date printable assignments to maximize your academic results in upcoming CBSE evaluations.
FAQs
You can download the latest chapter-wise printable worksheets for Class 8 Mathematics Chapter 07 Cubes and Cube Roots for free from StudiesToday.com. These have been made as per the latest CBSE curriculum for this academic year.
Yes, Class 8 Mathematics worksheets for Chapter 07 Cubes and Cube Roots focus on activity-based learning and also competency-style questions. This helps students to apply theoretical knowledge to practical scenarios.
Yes, we have provided solved worksheets for Class 8 Mathematics Chapter 07 Cubes and Cube Roots to help students verify their answers instantly.
Yes, our Class 8 Mathematics test sheets are mobile-friendly PDFs and can be printed by teachers for classroom.
For Chapter 07 Cubes and Cube Roots, regular practice with our worksheets will improve question-handling speed and help students understand all technical terms and diagrams.