Class 8 · Chapter 7

Cubes and Cube Roots

Perfect cubes and cube roots via prime factorisation.

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Tip: open the NCERT PDF for the original chapter text alongside the notes here.

Detailed theory

Cube of a natural number:

1, 8, 27, 64, 125, \ldots

n^3 = n\cdot n\cdot n

Key concepts & formulas

A perfect cube has each prime factor's exponent divisible by

3

\sqrt[3]{a\cdot b} = \sqrt[3]{a}\cdot\sqrt[3]{b}

Cube of a negative number is negative.

(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3

Every integer's cube is unique.