A Square and A Cube

About this chapter

A Square and A Cube is the opening chapter of Class 8 Ganita Prakash Part 1. It begins with Queen Ratnamanjuri's locker puzzle in which Khoisnam realises that lockers numbered 1, 4, 9, 16, 25, 36, 49, 64, 81 and 100 stay open because square numbers alone have an odd number of factors. From this hook the chapter builds two big ideas — square numbers and cube numbers — and their inverse operations, square root and cube root. Students explore patterns of perfect squares (last digits 0, 1, 4, 5, 6, 9; squares of n end with the same parity; n squared as the sum of the first n odd numbers; triangular pairs adding to squares), learn three methods for square roots (listing squares, repeated subtraction of odd numbers, prime factorisation in pairs), and then extend the same logic to cubes — 1, 8, 27, 64, … — meeting Ramanujan's Hardy–Ramanujan number 1729 and the Sanskrit terms varga and ghana. CTET Paper 2 Mathematics tests this chapter through pattern-spotting items, prime factorisation problems, square-root and cube-root estimation, perfect-square and perfect-cube identification, and pedagogy of teaching squares through area models. The four tests below — Practice 15, Quiz 15, Hard 15, Mastery 30 — cover all six big ideas at CTET depth.