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# Cubes and Cube Root class 8 Notes Mathematics

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## Class 8 Mathematics notes Chapter 7 Cubes and Cube Root

Download CBSE class 8th revision notes for chapter 7 Cubes and Cube Root in PDF format for free. Download revision notes for Cubes and Cube Root class 8 Notes and score high in exams. These are the Cubes and Cube Root class 8 Notes prepared by team of expert teachers. The revision notes help you revise the whole chapter 7 in minutes. Revision notes in exam days is one of the best tips recommended by teachers during exam days.

## CBSE Class 8 Revision Notes Maths 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.

## Cubes and Cube Root class 8 Notes Mathematics

Cubes and Cube Root class 8 Notes Mathematics. CBSE quick revision note for class-8 Mathematics, Chemistry, Math’s, Biology and other subject are very helpful to revise the whole syllabus during exam days. The revision notes covers all important formulas and concepts given in the chapter. Even if you wish to have an overview of a chapter, quick revision notes are here to do if for you. These notes will certainly save your time during stressful exam days.

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