Multiple choice

The smallest positive integer x, for which 945x2 = N3, where N is a natural number, is

  1. 49

  2. 25

  3. 35

  4. 9
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

945 = 3³ × 5 × 7. For 945x² to be a perfect cube N³, x² must provide the missing factors to make all exponents multiples of 3. We need one more 3, one more 5, and two more 7s. So x² = 3 × 5 × 7² = 735, giving x = √735 = 35. Verification: 945 × 35² = 945 × 1225 = 1157625, and 1157625^(1/3) = 105.

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