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ICSE-VIII-Mathematics

04: Cubes and Cube Roots Class 8 Maths

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  • #2
    Find which of the following are perfect cubes: (i) 243 (ii) 588 (iii) 1331 (iv) 24000 (v) 1728 (vi) 1938
    Ans : (i) 243

    ∵ 243 = 3 × 3 × 3 × 3
    = (3 × 3 × 3) × 3
    = 33 × 3
    ∴ 297 is not a perfect cube. (ii) 588

    588 = 2 × 2 × 7 × 7 × 3
    ∴ 588 is not a perfect cube. (iii) 1331

    ∵ 1331 = 11 × 11 × 11 = (11)3
    ∴ 1331 is perfect cube. (iv) 24000
    ∵ 24000 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 5 × 5 × 5
    = (2)3 × (2)3 × (5)3 × 3
    ∴ 24000 is not a perfect cube. (v) 1728

    ∵ 1728 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3
    = (2)3 × (2)3 × (3)3
    ∴ 1728 is a perfect cube. (vi) 1938
    1938 = 2 × 3 × 17 × 19
    1938 is not a perfect cube.
  • #2-i
    243
    Ans : 243

    ∵ 243 = 3 × 3 × 3 × 3
    = (3 × 3 × 3) × 3
    = 33 × 3
    ∴ 297 is not a perfect cube.
  • #2-ii
    588
    Ans : 588

    588 = 2 × 2 × 7 × 7 × 3
    ∴ 588 is not a perfect cube.
  • #2-iii
    1331
    Ans : 1331

    ∵ 1331 = 11 × 11 × 11 = (11)3
    ∴ 1331 is perfect cube.
  • #2-iv
    24000
    Ans : 24000
    ∵ 24000 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 5 × 5 × 5
    = (2)3 × (2)3 × (5)3 × 3
    ∴ 24000 is not a perfect cube.
  • #2-v
    1728
    Ans : 1728

    ∵ 1728 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3
    = (2)3 × (2)3 × (3)3
    ∴ 1728 is a perfect cube.
  • #2-vi
    1938
    Ans : 1938
    1938 = 2 × 3 × 17 × 19
    1938 is not a perfect cube.