Squares and
Square Roots
Complete chapter resources for CBSE Class 8 Maths — topic breakdown, key properties, sample questions, previous year board questions, and instant AI question paper generation.
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- Perfect square: n² where n is a natural number
- Square root (√): √(a²) = a, a ≥ 0
- Pythagorean triplet: (2m, m²−1, m²+1), m > 1
- Sum of first n odds: 1+3+5+...+(2n−1) = n²
- Unit-digit rule: perfect squares end in 0,1,4,5,6,9 only
- Long division: pairs of digits from right → quotient digit by digit
What this chapter covers
Chapter 6 introduces square numbers — natural numbers that are squares of other natural numbers — and explores their properties: the unit-digit pattern (squares end only in 0, 1, 4, 5, 6, or 9), the fact that between consecutive squares n² and (n+1)² there are exactly 2n non-square numbers, and the elegant identity that the sum of the first n odd natural numbers equals n². Students also learn to generate Pythagorean triplets using the formula (2m, m²−1, m²+1) for any natural number m > 1.
The chapter teaches two methods to find the square root of a number. The prime factorisation method works when the number can be neatly expressed as a product of prime pairs — students group primes in twos and multiply one from each pair. The long division method applies to any positive integer and to decimal numbers; it is the standard method for numbers where prime factorisation is tedious and for finding square roots to a specified number of decimal places.
Estimation of square roots without a calculator is another key skill — identifying the two consecutive perfect squares between which a given number lies, then narrowing in. Board questions in Class 8 and subsequent classes regularly test all these methods, and understanding square roots deeply is a prerequisite for the Pythagorean theorem, irrational numbers (Class 9), and quadratic equations (Class 10).
What's inside Chapter 6
As per NCERT Class 8 Mathematics (CBSE syllabus)
How this chapter fits in
Useful for setting question difficulty and cross-chapter papers.
Square Roots
Marks & question-type breakdown
Typical pattern based on CBSE Class 8 school and periodic assessment papers.
| Question type | Marks | Typical count | What's usually tested |
|---|---|---|---|
| MCQ / Objective | 1 | 1–2 | Identify perfect squares, unit-digit rule, Pythagorean triplet verification |
| Very Short Answer | 1–2 | 1 | Square root by prime factorisation for a given number |
| Short Answer | 3 | 1 | Long division method to 2 decimal places, or generating a Pythagorean triplet |
| Long Answer / Word Problem | 4–5 | 0–1 | Area/length problem requiring square root, or least number to be added/subtracted |
| Total (approximate) | 4–6 | 3–4 | Weightage varies across paper sets and terms |
8 sample questions — generated by MarksZen AI
Aligned to CBSE Class 8 Maths Chapter 6. Covers all question types across Easy, Medium, and Hard difficulty.
MarksZen AI creates a complete question paper with answer key in under 2 minutes.
From CBSE school examinations
Representative questions from Class 8 annual and periodic assessment papers — Squares and Square Roots chapter.
Create a board-aligned
question paper in 2 minutes.
Pick chapter, set the question-type mix and total marks — MarksZen AI generates the full paper with answer key. CBSE, ICSE, and all State Boards supported.
- All 4 topics of this chapter
- MCQ + short answer + word problems
- Answer key included
- PDF export ready