Class 8 Mathematics – Squares and Square Roots
These notes are prepared by Veezna Group of Institutes for Class 8 students. The chapter Squares and Square Roots is explained in a very easy manner with many solved examples, so students can understand concepts clearly and feel confident in exams.
1. Square Numbers
When a number is multiplied by itself, the result is called a square number.
Examples:
- 1 × 1 = 1 (1 is a square number)
- 2 × 2 = 4
- 5 × 5 = 25
Squares of the first few natural numbers:
- 1² = 1
- 2² = 4
- 3² = 9
- 4² = 16
- 5² = 25
2. Properties of Square Numbers
- The square of any natural number is always positive.
- Square numbers always end with 0, 1, 4, 5, 6, or 9.
- Squares of even numbers are even.
- Squares of odd numbers are odd.
Solved Example:
Is 4225 a square number?
Last digit of 4225 is 5. Only numbers ending with 5 can have squares ending with 25.
65² = 4225
Therefore, 4225 is a square number.
3. Square Roots
The square root of a number is a value which, when multiplied by itself, gives the original number.
Symbol: √
Examples:
- √4 = 2 (because 2 × 2 = 4)
- √25 = 5
- √81 = 9
4. Finding Square Roots by Prime Factorisation
Steps:
- Write the number as a product of prime factors.
- Make pairs of same factors.
- Take one factor from each pair.
Solved Example:
Find √144
144 = 2 × 2 × 2 × 2 × 3 × 3
Taking pairs: (2×2), (2×2), (3×3)
√144 = 2 × 2 × 3 = 12
5. Finding Square Roots by Repeated Subtraction
In this method, we subtract successive odd numbers from the given number until we get zero. The number of steps gives the square root.
Solved Example:
Find √16
16 − 1 = 15
15 − 3 = 12
12 − 5 = 7
7 − 7 = 0
Number of steps = 4
So, √16 = 4
Important Exam-Oriented Questions
Very Short Answer
- Find the square of 12.
- Write √49.
Short Answer
- Is 2025 a square number? Give reason.
- Find √196 by prime factorisation.
Long Answer
- Explain the properties of square numbers.
- Find the square root of 324 by prime factorisation method.
Key Points for Exams
- Square means number multiplied by itself.
- Square roots undo squares.
- Prime factorisation is the most common exam method.
- Write steps clearly to get full marks.
Prepared with care by Veezna Group of Institutes to support learning and exam preparation.
