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Cube and Cube Roots — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSCube and Cube Roots1 Mark
MCQ
Which among the following is a perfect cube?
  • A
    $400$
  • ✓
    $15625$
  • C
    $243$
  • D
    $9000$
✓

Answer

Correct option: B.
$15625$
$400 = 2 \times 2 \times 2 \times 2 \times 5 \times 5; 2 \times 5 \times 5$ remains after grouping into triplets.Therefore, it is not a perfect square.
$15625 = 5 \times 5 \times 5 \times 5 \times 5 \times 5$ In this factorization, nothing remains after grouping $S'$s in triplets. Therefore, it is a perfect square.
$243 = 3 \times 3 \times 3 \times 3 \times 3$ In this factorization $3 \times 3$ remains after grouping $3'$ in triplets. Hence, it is not a perfect square.
$9000 = 3 \times 3 \times 2 \times 2 \times 2 \times 5 \times 5 \times 5$ In this factorization $3 \times 3$ remains after groping $5's$ and $2's$ in triplets.
Hence, it is not a perfect. Square.

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