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Ayushree
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Asked: 2025-08-01T10:21:35+00:00 In:

Which of the following is the greatest? Explain your reasoning. (i) 67³ – 66³ (ii) 43³ – 42³ (iii) 67² – 66² (iv) 43² – 42²

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Use identity:
a³ – b³ = (a–b)(a² + ab + b²),
a² – b² = (a–b)(a + b).
(i) has largest numbers and cube difference. So, 67³ – 66³ is the greatest.

Class 8 Mathematics Ganita Prakash A Square and A Cube

Class 8 Mathematics Ganita Prakash Chapter 1 A Square and A Cube NCERT solutions

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    1 Answer

    1. Let’s compare using identities:
      a³ – b³ = (a–b)(a² + ab + b²)
      67³ – 66³ = 1(4489 + 4422 + 4356) = 13267
      43³ – 42³ = 1(1849 + 1806 + 1764) = 5419
      a² – b² = (a–b)(a + b)
      67² – 66² = 1(133) = 133
      43² – 42² = 1(85) = 85
      So, the greatest is 67³ – 66³

       

      For more NCERT Solutions for Class 8 Mathematics Ganita Prakash Chapter 1 A Square and A Cube Extra Questions & Answer:

      https://www.tiwariacademy.com/ncert-solutions/class-8/maths/ganita-prakash-chapter-1/

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