Class 8 Maths Square and Cube Root NCERT Questions (51 Marks) – Ganita Prakash | USP Indore

Class 8 Maths – Squares, Square Roots, Cubes and Cube Roots | NCERT Questions | USP Indore

This is a 28-question NCERT-based practice paper on Squares, Square Roots, Cubes and Cube Roots for Class 8 Maths (Ganita Prakash), prepared by Unique Study Point (USP), Indore. The paper carries 51 marks with a time limit of 30 minutes, and is based on the CBSE NCERT Ganita Prakash syllabus (Session 2026-27). All questions are directly from or based on NCERT exercises and are ideal for quick revision and chapter-wise practice.

Paper Overview

• 📘 Subject: Class 8 Mathematics (Ganita Prakash)
• 📗 Chapter: Squares, Square Roots, Cubes and Cube Roots
• 📙 Total Questions: 28
• 📕 Maximum Marks: 51
• ⏱️ Time Allowed: 30 Minutes
• ✅ Based on: NCERT Ganita Prakash | Session 2026-27

Topics Covered in This Question Paper

🔢 Part 1 – Squares and Square Roots (Q1 to Q16)

• Units digit rule for perfect squares – numbers ending in 0, 1, 4, 5, 6, or 9
• Identifying non-perfect squares by units digit (2, 3, 7, 8 rule)
• Which of the given squares have digit 6 in the units place? (38², 34², 46², 56², 74², 82²)
• Zeros in square of a number – if number ends in 3 zeros, square ends in 6 zeros
• Relation between triangular numbers and square numbers – pattern extension activity
• Square root of 64 – basic concept
• How to check if a number (like 576 or 327) is a perfect square; finding its square root
• Identifying non-perfect squares among 2032, 2048, 1027, 1089
• Last digit of 64², 108², 292², 36² – which has last digit 4?
• Given 125² = 15625, finding the value of 126² using identity
• Side of a square with area 441 m² – application of square root
• Smallest square number divisible by 4, 9, and 10 – using LCM method
• Smallest number to multiply 9408 to make it a perfect square; finding square root of product
• How many numbers lie between squares of 16 & 17, and 99 & 100?
• Pattern-based missing numbers: 1² + 2² + 2² = 3², 2² + 3² + 6² = 7², 3² + 4² + 12² = 13²…
• Sum of 10 consecutive odd numbers: 91 + 93 + 95 + 97 + 99 + 101 + 103 + 105 + 107 + 109 – shortcut method

🧊 Part 2 – Cubes and Cube Roots (Q17 to Q28)

• Cube root of 64
• Cube root of 512
• Cube root of 729
• Cube roots of 27000 and 10648
• What number to multiply 1323 to make it a perfect cube?
• True or False: The cube of any odd number is even
• True or False: There is no perfect cube that ends with 8
• True or False: The cube of a 2-digit number may be a 3-digit number
• True or False: The cube of a 2-digit number may have seven or more digits
• True or False: Cube numbers have an odd number of factors
• Which is greatest among 67³ − 66³, 43³ − 42³, 67² − 66², 43² − 42²? – with reasoning
• Challenge: Arrange numbers 1 to 17 so every adjacent pair adds up to a perfect square

All 28 Questions at a Glance

Q1 [1M]. If a number ends in 0, 1, 4, 5, 6 or 9, is it always a perfect square?

Q2 [1M]. Write 5 numbers whose units digit tells you they are NOT perfect squares.

Q3 [5M]. Which of 38², 34², 46², 56², 74², 82² have the digit 6 in the units place?

Q4 [1M]. If a number has 3 zeros at the end, how many zeros will its square have?

Q5 [2M]. Relation between triangular numbers and square numbers – extend the dot pattern.

Q6 [2M]. What is the square root of 64?

Q7 [2M]. How to find if 576 or 327 is a perfect square? Find square root if it is.

Q8 [3M]. Which of 2032, 2048, 1027, 1089 are NOT perfect squares?

Q9 [1M]. Which of 64², 108², 292², 36² has last digit 4?

Q10 [2M]. Given 125² = 15625, find the value of 126².

Q11 [1M]. Find the side of a square with area 441 m².

Q12 [3M]. Smallest perfect square divisible by 4, 9, and 10.

Q13 [2M]. Smallest multiplier for 9408 to make it a perfect square; find square root of result.

Q14 [2M]. Numbers between squares of (i) 16 and 17, (ii) 99 and 100.

Q15 [2M]. Fill missing numbers: 4² + 5² + 20² = (__)², 9² + 10² + (__)² = (__)²

Q16 [2M]. Find the sum 91 + 93 + 95 + 97 + 99 + 101 + 103 + 105 + 107 + 109 without calculation.

Q17 [1M]. Cube root of 64.

Q18 [1M]. Cube root of 512.

Q19 [1M]. Cube root of 729.

Q20 [2M]. Cube roots of 27000 and 10648.

Q21 [1M]. What number multiplied by 1323 gives a perfect cube?

Q22 [1M]. True/False: Cube of any odd number is even.

Q23 [1M]. True/False: No perfect cube ends with 8.

Q24 [1M]. True/False: Cube of a 2-digit number may be a 3-digit number.

Q25 [1M]. True/False: Cube of a 2-digit number may have seven or more digits.

Q26 [1M]. True/False: Cube numbers have an odd number of factors.

Q27 [3M]. Which is greatest among 67³ − 66³, 43³ − 42³, 67² − 66², 43² − 42²? Explain.

Q28 [5M]. Arrange numbers 1 to 17 so every adjacent pair sums to a perfect square. Can it be done in more than one way?

Key Concepts Tested in This Paper

• Perfect Square Rule: A number can be a perfect square only if its units digit is 0, 1, 4, 5, 6, or 9. Numbers ending in 2, 3, 7, or 8 are NEVER perfect squares.
• Zeros Rule: If a number has n zeros at the end, its square will have 2n zeros.
• Triangular Numbers and Squares: Sum of two consecutive triangular numbers is always a perfect square. e.g., 1 + 3 = 4 = 2²
• Sum of Consecutive Odd Numbers: Sum of first n odd numbers = n². e.g., 91 + 93 + … + 109 = sum of 10 consecutive odd numbers = 100² = 10000 (shortcut)
• Numbers Between Consecutive Squares: Between n² and (n+1)² there are always 2n numbers.
• Prime Factorisation Method: Used to find square root and to identify smallest multiplier/divisor for perfect square or perfect cube.
• Cube Root: ∛64 = 4, ∛512 = 8, ∛729 = 9, ∛27000 = 30, ∛10648 = 22
• Successive Difference Identity: (n+1)³ − n³ = 3n² + 3n + 1; used to compare differences of cubes and squares.

Important FAQs – Class 8 Maths Squares and Cubes

Q. How do you know if a number is NOT a perfect square just by looking at it?
Ans. If the units digit of a number is 2, 3, 7, or 8, it is definitely NOT a perfect square. For example, 2032, 2048, and 1027 are not perfect squares because their units digits are 2, 8, and 7 respectively.

Q. How many numbers lie between n² and (n+1)²?
Ans. There are always 2n numbers between n² and (n+1)². For example, between 16² = 256 and 17² = 289, there are 2 × 16 = 32 numbers. Between 99² and 100², there are 2 × 99 = 198 numbers.

Q. What is the shortcut to find the sum 91 + 93 + 95 + … + 109?
Ans. These are 10 consecutive odd numbers. The sum of the first n odd numbers is n². Here, 91 to 109 are the 46th to 55th odd numbers, and their sum equals 55² − 45² = 3025 − 2025 = 1000. Alternatively, average × count = 100 × 10 = 1000.

Q. How to find the smallest number to multiply a number to make it a perfect square?
Ans. Find the prime factorisation of the number. Any prime factor with an odd power needs one more of itself to make the power even (perfect square). The product of all such unpaired primes is the smallest multiplier needed.

Q. What is the cube root of 27000?
Ans. 27000 = 27 × 1000 = 3³ × 10³ = (3 × 10)³ = 30³. Therefore ∛27000 = 30.

Q. Is the cube of any odd number even? (True or False)
Ans. False. The cube of any odd number is always odd. For example, 3³ = 27 (odd), 5³ = 125 (odd).

Q. Is there a perfect cube that ends with 8?
Ans. Yes. 2³ = 8, 12³ = 1728, 22³ = 10648. So the statement \\\"there is no perfect cube ending with 8\\\" is False.

About Unique Study Point (USP), Indore

Unique Study Point (USP) is a trusted coaching institute in Amitesh Nagar, Indore, Madhya Pradesh, offering quality education for Classes VI to X in Mathematics, Science, and Social Science. All study materials are prepared by experienced educators and strictly follow the latest CBSE-NCERT Ganita Prakash syllabus 2026-27.

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