📘 Class 8 · Mathematics

Chapter 6: Square Roots and Cube Roots

6 lessons

The square root of a number, multiplied by itself, gives that number back; the cube root does the same multiplied by itself three times. This chapter covers recognising perfect squares and cubes, and finding roots by prime factorisation and by long division — 225 breaks down as 3²×5², giving a square root of 3×5=15.

1
Introduction to Square Numbers
Properties of square numbers and interesting patterns in squares.
 2
Exercise 6.1 — Square Properties
Problems based on properties of square numbers.
 3
Exercise 6.2 — Prime Factorisation Method
Finding the square root by prime factorisation method.
 4
Exercise 6.3 — Division Method
Finding square root by division method, square roots of decimal numbers.
 5
Exercise 6.4 — Cubes and Cube Roots
Cubes and cube roots with interesting patterns.
 6
Exercise 6.5 — Cube Root Methods
Cube roots by prime factorisation and estimating cube roots.

Why it pays off later

Square roots reappear constantly from here — inside Class 9's irrational numbers (most non-perfect-square roots are irrational), inside the Pythagorean theorem, and throughout Class 10's quadratic equations and trigonometry. Fluency here makes all three noticeably easier later.

In the long-division method, misplacing the decimal point or pairing digits incorrectly from it is the most common source of a wrong answer — and it's worth checking early whether a number even has a "nice" whole-number root before assuming it does.