What's the smallest value of the natural number x(x ≠ 0), so that 280x is a perfect square?

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  • rotchm
    Lv 7
    2 years ago
    Best Answer

    280 = 2^3 * 5 * 7. You want that

    2^3 * 5 * 7* x = n²

    For this, all powers on the LHS bust be multiples of 2 [why?].

    So you need an extra 2 to make 2^4, an extra 5 to make 5² and an extra 7 to make 7² .

    Recap: An extra 2 & 5 & 7.

    So, whats the answer for x?

    Done!

    • rotchm
      Lv 7
      2 years agoReport

      Yes, 280*280 is a perfect square. But as you notice, its not the *smallest* as requested in the question.

  • Dixon
    Lv 7
    2 years ago

    You need to make it so that 280x has paired prime factors, then it will be a perfect square.

    280 = (2 x 2) x 2 x 5 x 7 which has one pair of twos but everything else is unpaired.

    So if you put in another 2, 5 and 7 it will become square.

    Thus x = 70

    • Eduardo
      Lv 4
      2 years agoReport

      Could you check the comment I made on rotchm's answer? And thanks for helping.

  • 2 years ago

    Ans. x=70

  • Ian H
    Lv 7
    2 years ago

    70 *280 = 140^2

    Extra 2 & 5 & 7.was a good way to establish that

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