Mathematics · Class 8
Squares and Square Roots
Perfect squares, square-root by prime factorisation and long division.
4 sections15–25 min read6 MCQs · 2 examples
Chapter Overview
Square numbers are n². Learn properties of squares, Pythagorean triples, finding square roots by prime factorisation and division method — used in geometry and science.
Square Numbers
- 1, 4, 9, 16, 25, ... — n × n
- Unit digit of square: 0,1,4,5,6,9 only
- Square of odd/even is odd/even
Square Root
Definition
√a = b if b² = a
Prime factorisation
Make pairs of equal factors
Division Method
Long division style for finding √ of large numbers like 2304. Group digits in pairs from right.
Solved Examples
Step-by-step solutions — read each step before checking the final answer.
Example 1: Square Root by Factors
Find √144.
- 1144 = 12²
- 2Or 2⁴×3² → pairs
Answer
12
Example 2: Check Perfect Square
Is 235 a perfect square?
- 1Unit digit 5 — can be square
- 2√235 ≈ 15.3 — not integer
Answer
No, 235 is not a perfect square
Key Points to Remember
- ✓ √ of product = product of √s for perfect squares
- ✓ Smallest 3-digit square is 100
- ✓ Pythagorean: 3²+4²=5²
Exam Tips
- • Make prime factor pairs for square roots
- • Estimate √ to verify answer
Practice MCQs — Squares and Square Roots
Test your understanding with topic-wise multiple choice questions. Explanations appear after each answer.
Question 1 of 6Score: 0/0
Square of 15 is: