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 ...
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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 ...
Yes, 3375 is a perfect cube. Its prime factorisation is 3 × 3 × 3 × 5 × 5 × 5. These group as (3 × 5)³ = 15³. So, 3375 is a cube and its cube root is 15. Class ...
4104 = 2³ + 16³ = 9³ + 15³ 13832 = 2³ + 24³ = 18³ + 20³ These are called taxicab numbers, which are expressible as the sum of two positive cubes in two distinct ways. Class 8 Mathematics Chapter ...
No, a cube cannot end with exactly two zeros. If a number ends in two zeros, it must be divisible by 100. Its cube will end with at least three zeros, because the number gets multiplied three times. Class 8 Mathematics ...