Which of the following statements is INCORRECT?

The square of every prime number is prime

There are 2n numbers between n² and (n+1)²

A perfect square never ends in 7

The square of an odd number is odd

Squares and Square Roots — Class 8 MCQs with Answers

Class 8 CBSE Mathematics · Chapter 105

Pre-2026 syllabusThis chapter is from the older NCERT book. See the 2026-27 Class 8 Mathematics chapters →

72 practice questions · 24 Easy · 24 Medium · 24 Hard · Updated 17 Sep 2026

Practise the most important Class 8 CBSE Mathematics questions from Chapter 105, "Squares and Square Roots". You get 9 timed quizzes made from 72 NCERT-based MCQs, with answers and explanations. The questions are split into 24 Easy, 24 Medium and 24 Hard. Warm up on the basics, then move on to the exam-level questions that set top scorers in CBSE Board exams apart.

To score well in "Squares and Square Roots", focus on fast problem-solving, formula recall and step-by-step working. Each MCQ here is timed and uses exam-style marking (+4 correct, −1 wrong, 0 skipped). This trains you to stay accurate under time pressure, as real papers need. Every question has a short explanation, so a wrong answer becomes a quick lesson. It is the fastest way to fix gaps before a test.

Use this chapter for focused revision. Start with the Easy set to check your basics on Squares and Square Roots, then move to Medium and Hard to practise applying them. Your accuracy, streaks and XP save automatically. This chapter also adds to your overall Class 8 Mathematics mastery score. 14 sample questions are solved in full below, with the answer and a worked explanation. Sign in free to start practising.

Key concepts: Squares and Square Roots (Class 8 Mathematics)

This chapter covers perfect squares and their properties, and finding square roots by prime factorisation and the long-division method.

Perfect square: A number that is the square of an integer, e.g. 1, 4, 9, 16; it never ends in 2, 3, 7 or 8.
Properties of squares: The square of an even number is even, of an odd number is odd; there are 2n non-perfect-squares between n² and (n+1)².
Square root: The number which, when multiplied by itself, gives the original number; √(a²) = a.
By prime factorisation: Pair the equal prime factors; the product of one factor from each pair gives the square root.

1 more key concept, 2 formulas, exam tips — free with sign-in.

Squares and Square Roots — important questions & MCQs with answers (Class 8 Mathematics)

14 solved questions from this chapter's difficulty levels, each with its answer and explanation. The other 58 are timed and scored when you sign in.

Q1Easy
Square of 12:
A.144✓ Correct
B.24
C.122
D.169
Answer: A. 144
Explanation: 12² = 144.
Q2Easy
√81 =
A.81
B.8
C.7
D.9✓ Correct
Answer: D. 9
Explanation: 9² = 81.
Q3Easy
What is the square of 15?
A.125
B.255
C.225✓ Correct
D.205
Answer: C. 225
Explanation: 15² = 15 × 15 = 225.
Q4Easy
√144 =
A.14
B.12✓ Correct
C.16
D.24
Answer: B. 12
Explanation: 12² = 144, so √144 = 12.
Q5Easy
Which of these is a perfect square?
A.50
B.63
C.49✓ Correct
D.45
Answer: C. 49
Explanation: 49 = 7², so it is a perfect square.
Q6Easy
√64 =
A.8✓ Correct
B.6
C.7
D.9
Answer: A. 8
Explanation: 8² = 64, so √64 = 8.
Q7Medium
Last digit of squares is never:
A.5, 6, 9
B.0,1,4
C.2, 3, 7, 8✓ Correct
D.All digits
Answer: C. 2, 3, 7, 8
Explanation: Squares end in 0,1,4,5,6,9.
Q8Medium
Square root of 196 by prime factorisation:
A.18
B.12
C.16
D.14✓ Correct
Answer: D. 14
Explanation: 196 = 2²·7² ⇒ √196 = 14.
Q9Medium
By what smallest number should 252 be multiplied to make it a perfect square?
A.7✓ Correct
B.3
C.5
D.2
Answer: A. 7
Explanation: 252 = 2²·3²·7; the unpaired 7 must be multiplied, so the answer is 7.
Q10Medium
Find √324 by prime factorisation.
A.16
B.18✓ Correct
C.14
D.22
Answer: B. 18
Explanation: 324 = 2²·3⁴ = (2·3²)² , so √324 = 18.
Q11Medium
By what smallest number should 180 be divided to make it a perfect square?
A.3
B.9
C.4
D.5✓ Correct
Answer: D. 5
Explanation: 180 = 2²·3²·5; dividing by the unpaired 5 gives 36, a perfect square.
Q12Hard
Number of digits in square of 25:
A.2
B.4
C.5
D.3 (625)✓ Correct
Answer: D. 3 (625)
Explanation: n-digit number's square has 2n or 2n−1 digits.
Q13Hard
√1024 =
A.34
B.30
C.32✓ Correct
D.28
Answer: C. 32
Explanation: 32² = 1024.
Q14Hard
Which of the following statements is INCORRECT?
A.There are 2n numbers between n² and (n+1)²
B.A perfect square never ends in 7
C.The square of every prime number is prime✓ Correct
D.The square of an odd number is odd
Answer: C. The square of every prime number is prime
Explanation: The square of a prime is not prime (e.g. 5² = 25 = 5·5); the other statements are all true.

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Squares and Square Roots — FAQs

What are the key concepts in Class 8 Mathematics Squares and Square Roots?+

This chapter covers perfect squares and their properties, and finding square roots by prime factorisation and the long-division method. Key ideas include Perfect square, Properties of squares, Square root, By prime factorisation.

What does Class 8 Mathematics Chapter 105 (Squares and Square Roots) cover on XamBaaz?+

It has 72 NCERT-based MCQs on "Squares and Square Roots": 24 Easy, 24 Medium and 24 Hard. Together they make 9 timed quizzes, and you never get the same set twice. Every question has an instant explanation. They help you prepare for CBSE Board exams.

Are these "Squares and Square Roots" questions free to practise?+

Yes. Sign in with Google to practise "Squares and Square Roots" free. Full unlimited access is ₹999/year on a launch offer until 1 December 2026. No chapter is charged separately.

How should I revise "Squares and Square Roots" for the exam?+

Start with the Easy quiz to check your basics, then try Medium and Hard to practise applying them. There are 9 timed quizzes on this chapter, so you can come back for a fresh set instead of one you have seen. Read each explanation, retry the questions you miss, and track your accuracy until it stays high.

Are these "Squares and Square Roots" MCQs available with answers?+

Yes. 14 sample questions are shown here in full, each with the correct option and a step-by-step "Why" explanation. Sign in free with Google to start practising, with instant scoring.

Is there negative marking in the "Squares and Square Roots" quizzes?+

Yes. The timed quizzes use exam-style marking: +4 for a right answer, −1 for a wrong one and 0 for a skip. MHT-CET and CBSE board papers have no negative marking. Our mocks for those are scored their way.

What are the important questions from Squares and Square Roots (Class 8 Mathematics)?+

The questions that matter most test Perfect square, Properties of squares, Square root, By prime factorisation. This page shows 14 solved important MCQs with answers and explanations; all 72 questions on the chapter are available as timed quizzes once you sign in.

Is there an online quiz for Squares and Square Roots?+

Yes — Class 8 Mathematics Squares and Square Roots has timed online quizzes at Easy, Medium and Hard levels, with instant scoring and a worked explanation on every question. The first quiz on the chapter is free.

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