Squares and Square Roots (NCERT Ch. 6)

• Identify perfect squares and their properties.
• Find the square root of a perfect square using prime factorisation and the long division method.
• Estimate square roots of non-perfect squares.

1. A perfect square is the square of a whole number (1, 4, 9, 16, 25, ...).
2. A number ending in 2, 3, 7, or 8 is never a perfect square.
3. Square root is the inverse operation of squaring: if n² = m, then √m = n.
4. Prime factorisation method: pair up identical prime factors; the square root is the product of one factor from each pair.

Find the square root of 144 using prime factorisation.

144 = 2 x 2 x 2 x 2 x 3 x 3 = (2x2)  x (2x2) x (3x3)...
Pairs: (2,2), (2,2), (3,3) -> take one from each pair: 2 x 2 x 3 = 12
√144 = 12

• Forgetting that a perfect square's prime factorisation must have EVERY prime in pairs (if not, it's not a perfect square).
• Confusing squaring (n²) with square rooting (√n) — they are inverse operations.
• Assuming all numbers ending in specific digits are always/never perfect squares without checking the actual rule.

• Is 128 a perfect square?
• Find √225 using prime factorisation.

Open the Practice tab for graded questions on Squares and Square Roots (NCERT Ch. 6).