CBSE Class 8 Maths Chapter 1: A Square and A Cube — Assertion & Reason
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The following Assertion and Reason questions are based on Chapter 1: A Square and a Cube from the NCERT Class 8 Mathematics textbook. Each question has four options - read both the Assertion (A) and Reason (R) carefully before selecting your answer.
How to attempt Assertion & Reason questions:
(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.
(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.
Assertion & Reason Questions
1
Assertion (A): A natural number has an odd number of positive factors exactly when it is a perfect square.
Reason (R): Factors usually pair, but a square has one unpaired factor equal to its square root.
Reason (R): Factors usually pair, but a square has one unpaired factor equal to its square root.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. The self-paired divisor makes the factor count odd.
2
Assertion (A): The numbers 1, 4, 9 and 16 are perfect squares.
Reason (R): The number 27 is a perfect cube.
Reason (R): The number 27 is a perfect cube.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but the cube fact does not explain the listed squares.
3
Assertion (A): An integer square cannot end in the digit 2.
Reason (R): The units digit of a square can be any digit from 0 to 9.
Reason (R): The units digit of a square can be any digit from 0 to 9.
Answer: (c)
A is true, but R is false. Integer squares can end only in 0, 1, 4, 5, 6 or 9.
4
Assertion (A): Every number ending in 6 is a perfect square.
Reason (R): Some nonsquares, such as 26, also end in 6.
Reason (R): Some nonsquares, such as 26, also end in 6.
Answer: (d)
A is false, but R is true. An allowed units digit is necessary but not sufficient.
5
Assertion (A): The difference between consecutive squares n squared and (n + 1) squared is 2n + 1.
Reason (R): Expanding (n + 1) squared - n squared gives 2n + 1.
Reason (R): Expanding (n + 1) squared - n squared gives 2n + 1.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. The algebra verifies the odd-number pattern.
6
Assertion (A): The sum of the first n odd natural numbers is n squared.
Reason (R): The cube of an odd integer is odd.
Reason (R): The cube of an odd integer is odd.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but parity of cubes does not explain the sum of odd numbers.
7
Assertion (A): There are exactly n natural numbers between n squared and (n + 1) squared.
Reason (R): Their difference is 2n + 1.
Reason (R): Their difference is 2n + 1.
Answer: (c)
A is true, but R is false. The count strictly between them is 2n, not n.
8
Assertion (A): A perfect square may have an odd number of trailing zeros.
Reason (R): Squaring doubles the exponent of every prime factor, including factors of 10.
Reason (R): Squaring doubles the exponent of every prime factor, including factors of 10.
Answer: (d)
A is false, but R is true. A nonzero perfect square has an even number of trailing zeros.
9
Assertion (A): If the prime factorisation of a number has only even exponents, the number is a perfect square.
Reason (R): Its square root is obtained by halving all prime exponents.
Reason (R): Its square root is obtained by halving all prime exponents.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Pairing identical prime factors produces an integer root.
10
Assertion (A): The positive square root of 441 is 21.
Reason (R): The cube root of 343 is 7.
Reason (R): The cube root of 343 is 7.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are correct, but the cube-root fact does not explain the first value.
11
Assertion (A): The positive square root of 250 lies between 15 and 16.
Reason (R): Its exact value is 15.
Reason (R): Its exact value is 15.
Answer: (c)
A is true, but R is false. Since 225 is less than 250 and 256 is greater, the root lies strictly between them.
12
Assertion (A): Every perfect square has only one integer square root.
Reason (R): A positive perfect square has a positive and a negative integer square root.
Reason (R): A positive perfect square has a positive and a negative integer square root.
Answer: (d)
A is false, but R is true. For example, both 8 and -8 square to 64.
13
Assertion (A): The cube of an even integer is even.
Reason (R): An even integer contains a factor 2, so its cube contains a factor 8.
Reason (R): An even integer contains a factor 2, so its cube contains a factor 8.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. The factor 2 remains after cubing.
14
Assertion (A): The cube of an odd integer is odd.
Reason (R): A cube may be represented as n x n x n.
Reason (R): A cube may be represented as n x n x n.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but the notation alone does not explain parity.
15
Assertion (A): A number ending in 2 has a cube ending in 6.
Reason (R): The units digit of 2 cubed is 8.
Reason (R): The units digit of 2 cubed is 8.
Answer: (c)
A is true, but R is false. A cube of a number ending in 2 ends in 8.
16
Assertion (A): The cube root of 1000 is 100.
Reason (R): Ten cubed equals 1000.
Reason (R): Ten cubed equals 1000.
Answer: (d)
A is false, but R is true. The cube root is 10.
17
Assertion (A): A perfect cube has prime exponents that are multiples of 3.
Reason (R): Grouping equal prime factors in triples produces its integer cube root.
Reason (R): Grouping equal prime factors in triples produces its integer cube root.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Each triple contributes one copy of the prime to the root.
18
Assertion (A): The number 729 is both a perfect square and a perfect cube.
Reason (R): It equals 27 squared and 9 cubed.
Reason (R): It equals 27 squared and 9 cubed.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both identities are true, but listing them verifies rather than explains the general intersection of squares and cubes.
19
Assertion (A): If a number is a perfect square, it must also be a perfect cube.
Reason (R): The number 16 is a square but not an integer cube.
Reason (R): The number 16 is a square but not an integer cube.
Answer: (c)
A is true, but R is false. The counterexample disproves the assertion.
20
Assertion (A): The cube root of a negative number is never real.
Reason (R): The cube of a negative integer is negative.
Reason (R): The cube of a negative integer is negative.
Answer: (d)
A is false, but R is true. Odd roots of negative numbers are real; for example, cube root of -8 is -2.
❓ Frequently Asked Questions
What is covered in CBSE Class 8 Maths Chapter 1 A Square and A Cube?
This chapter covers all key topics from A Square and A Cube as per CBSE 2026-27 syllabus.
Is this Assertion & Reason useful for CBSE board exams?
Yes, designed for CBSE Class 8 board exam preparation covering the complete syllabus.
Are these CBSE Class 8 Maths Assertion & Reason updated for 2026-27?
Yes, all content at eBookPublisher is updated as per the latest 2026-27 CBSE syllabus.
How many chapters are in CBSE Class 8 Maths?
All chapters of CBSE Class 8 Maths are covered at eBookPublisher with free Assertion & Reason for each chapter.
Can I study A Square and A Cube online for free?
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