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Math Help - square numbers

  1. #1
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    Cool square numbers

    When a natural number is multiplied by itself,the result is a square number. Some examples of square numbers are 1,4,9,16 and 25.

    How many square numbers are there between 1,000 and 2000?
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  2. #2
    Senior Member vincisonfire's Avatar
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    Reply

    31^2 = 961
    45^2 = 2025
    44-31 = 13 perfect squares between 1000 and 2000
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  3. #3
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    Hello, fecoupefe!

    When a natural number is multiplied by itself,the result is a square number.
    Some examples of square numbers are 1, 4, 9, 16 and 25.

    How many square numbers are there between 1,000 and 2000?

    Since \sqrt{1000}\approx 31.62 and \sqrt{2000} \approx 44.72

    . . the squares are: . 32^2,\:33^2,\:34^2,\hdots,\:44^2

    There are 13 square numbers between 1000 and 2000.

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  4. #4
    Super Member 11rdc11's Avatar
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    Quote Originally Posted by fecoupefe View Post
    When a natural number is multiplied by itself,the result is a square number. Some examples of square numbers are 1,4,9,16 and 25.

    How many square numbers are there between 1,000 and 2000?
    There are 13 square numbers between 1000 and 2000.

    here is why

    \sqrt{1000}~=~31.62277

    \sqrt{2000}~=~44.721

    so
    44-31~=~13
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