CBSE Class 8 Maths Revision Notes Chapter 7 – Cubes and Cube Roots

Revision Notes for CBSE Class 8 Maths Chapter 7 – Free PDF Download

Free PDF download of Class 8 Maths Chapter 7 – Cubes and Cube Roots Revision Notes & Short Key-notes prepared by expert Maths teachers from latest edition of CBSE(NCERT) books. All Chapter 7 – Cubes and Cube Roots Revision Notes to help you to revise complete Syllabus and Score More marks.
Maths NCERT Solutions for Class 8

Quick Revision Notes

• 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√3 denotes cube root. For example 327−−√=3327=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.