Tuesday 23 December 2014

Square of a Natural Number



      Can you name the square of a natural number that is twice the square of some other natural number?

Answer: There is no such natural number.

           If a is a natural number, then 2A² cannot be a square since A² can be represented as the product of pairs of prime factors. There is no ‘extra’ factor of two to ‘pair up with ‘the factor of two in 2A².

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