(i) False – cube of odd is odd. (ii) False – 2³ = 8. (iii) True – 5³ = 125. (iv) True – 99³ = 970299 (v) False – cube numbers (unless cube of square) have even factors. Class 8 Mathematics ...
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Prime factorisation of 1323 = 3³ × 7². To make it a cube, we need one more 7. So, multiply by 7. 1323 × 7 = 9261 and 9261 = 21³. So, required number = 7. Class 8 Mathematics Textbook Chapter ...
27000 = 30³, so cube root is 30. 10648 = 22³, so cube root is 22. We find this either by prime factorisation or by recognising these as perfect cubes. Both values are exact and whole numbers. Class 8 NCERT Ganita ...
Successive differences of perfect cubes eventually become equal at the third level. This shows that cubes grow at a rate where third-order differences are constant, which is why they’re called third-degree polynomials in algebra. Class 8 NCERT Ganita Prakash Chapter 1 ...
No, 500 is not a perfect cube. Its prime factors are 2 × 2 × 5 × 5 × 5. The 2s cannot be grouped into a triplet. So, 500 is not a cube because all factors must occur in ...