Question

The area of a square is 16 square units. Since 42 = 16 and (-4)2 = 16, both 4 and -4
are square roots for 16. Explain why both square roots for 16, the area of the square,
cannot be the length of each side of the square.

Answer 1

It is true that (-4)^2 = 16; however, it doesn't make sense to have a square with a negative side lengths. Lengths and distances must be positive numbers.

So in many problems, we'll just ignore the negative solution to equations like x^2 = 16. It makes sense to only consider x = 4 for situations like this.

Answer 2

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