Class 8 · Chapter 1

A Square and A Cube

Squares, square roots, cubes, and cube roots.

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Ganita Prakash · Class 8 Part 1 (2026-27)

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Detailed theory

Square numbers:

1, 4, 9, 16, \ldots

. Sum of first

n

odd numbers

= n^2

(n+1)^2 - n^2 = 2n+1

Key concepts & formulas

**Square** of

n

n^2

. **Cube** of

n

n^3

**Square root**

\sqrt n

: number whose square is

n

**Cube root**

\sqrt[3] n

: number whose cube is

n

Perfect squares end in 0, 1, 4, 5, 6, 9 (never 2, 3, 7, 8).

Prime factorisation makes root-finding systematic.