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Why are perfect squares never negative?

Updated: 4/28/2022
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13y ago

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A perfect square is an integer (whole number) times itself. E.g. 3*3 = 9, or -4*-4 = 16.

A negative number times a negative number is a positive number. This means a negative number times itself would be positive.

It also holds true for all squares, not just perfect squares. E.g., -1.3 * -1.3 = 1.69 (which is positive).

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Q: Why are perfect squares never negative?
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Can negative numbers be perfect squares?

yes


Can you write every integer as the sum of two nonzero perfect squares?

No.First of all, you can't write negative numbers as sums of perfect squares at all - since all perfect squares are positive.Second, for natural numbers (1, 2, 3...) you may need up to 4 perfect squares: http://en.wikipedia.org/wiki/Lagrange's_four-square_theoremNo.First of all, you can't write negative numbers as sums of perfect squares at all - since all perfect squares are positive.Second, for natural numbers (1, 2, 3...) you may need up to 4 perfect squares: http://en.wikipedia.org/wiki/Lagrange's_four-square_theoremNo.First of all, you can't write negative numbers as sums of perfect squares at all - since all perfect squares are positive.Second, for natural numbers (1, 2, 3...) you may need up to 4 perfect squares: http://en.wikipedia.org/wiki/Lagrange's_four-square_theoremNo.First of all, you can't write negative numbers as sums of perfect squares at all - since all perfect squares are positive.Second, for natural numbers (1, 2, 3...) you may need up to 4 perfect squares: http://en.wikipedia.org/wiki/Lagrange's_four-square_theorem


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