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 $3\sqrt{}$ denotes cube root. For example $3\sqrt{27}=3$
• 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.