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
Jump to the 6 solved questions
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 top scorers in CBSE Board exams get right.
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 helps you stay accurate when time is short, just 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. Try the 6 sample questions below: tap an option to see the answer and a worked explanation. Sign in free to start practising.
Squares and Square Roots — important questions & MCQs with answers (Class 8 Mathematics)
6 solved questions from this chapter's difficulty levels, each with its answer and explanation. Tap an option to check yourself.
0 of 6 answered
- Q1 of 6Easy
Square of 12:
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Answer: 144
Explanation: 12² = 144.
- Q2 of 6Easy
√81 =
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Answer: 9
Explanation: 9² = 81.
- Q3 of 6Medium
Last digit of squares is never:
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Answer: 2, 3, 7, 8
Explanation: Squares end in 0,1,4,5,6,9.
- Q4 of 6Medium
Square root of 196 by prime factorisation:
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Answer: 14
Explanation: 196 = 2²·7² ⇒ √196 = 14.
- Q5 of 6Hard
Number of digits in square of 25:
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Answer: 3 (625)
Explanation: n-digit number's square has 2n or 2n−1 digits.
- Q6 of 6Hard
√1024 =
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Answer: 32
Explanation: 32² = 1024.
Squares and Square Roots notes: key concepts (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.
- Long-division method
- Used to find the square root of large numbers and of decimals.
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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, Long-division method.
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. One year from the day you pay. You stay in Class 8 till 31 March; on 1 April your account moves up to Class 9 and the rest of your year carries over. 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. 6 sample questions are on this page with answers: tap an option, or "Show answer", to see the correct option and a step-by-step 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, Long-division method. This page shows 6 solved important MCQs with answers and explanations. Sign in to practise all 72 questions on the chapter as timed quizzes.
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.
Are there question answers and extra questions for Squares and Square Roots (Class 8 Mathematics)?+
Yes. This page has 6 solved questions on Squares and Square Roots, each with the correct answer and a short explanation. Sign in to practise all 72 questions on the chapter as timed quizzes.