Cubes and Cube Roots - Revision Notes

CBSE Class 8 Mathematics
Revision Notes
Chapter – 7
Cubes and Cube Root
  • Cube number: Number obtained when a number is multiplied by itself three times. 23 = 2 x 2 x 2 = 8, 33 = 3 x 3 x 3=27, etc.
  • Numbers like 1729, 4104, 13832, are known as Hardy – Ramanujan Numbers. They can be expressed as sum of two cubes in two different ways.
  • Numbers obtained when a number is multiplied by itself three times are known as cube numbers. For example 1, 8, 27, ... etc.
  • If in the prime factorisation of any number each factor appears three times, then the number is a perfect cube.
  • The symbol 3 denotes cube root. For example 327=3
  • Perfect Cube: A natural number is said to be a perfect cube if it is the cube of some natural number. Example: 8 is perfect cube, because there is a natural number 2 such that 8 = 23, but 18 is not a perfect cube, because there is no natural number whose cube is 18.
  • The cube of a negative number is always negative.
  • Properties of Cube of Number:
    (i) Cubes of even number are even.
    (ii) Cubes of odd numbers are odd.
    (iii) The sum of the cubes of first n natural numbers is equal to the square of their sum.
    (iv) Cubes of the numbers ending with the digits 0, 1, 4, 5, 6 and 9 end with digits 0, 1, 4, 5, 6 and 9 respectively.
    (v) Cube of the number ending in 2 ends in 8 and cube of the number ending in 8 ends in 2.
    (vi) Cube of the number ending in 3 ends in 7 and cube of the number ending in 7 ends in 3.