Each side of the square measures Convince Me! Why are there two possible solutions to the equation $$ s^{2}=100 $$ ? Explain why only one of the solutions is valid in this situation.

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1. The equation given is $$ s^2 = 100 $$. To solve for $$ s $$, we take the square root of both sides:

$$
   s = \sqrt{100} \quad \text{or} \quad s = -\sqrt{100}
   $$

2. This yields two potential solutions:

$$
   s = 10 \quad \text{or} \quad s = -10
   $$

3. Although both $$ s = 10 $$ and $$ s = -10 $$ satisfy the equation $$ s^2 = 100 $$ mathematically, in the context of a square’s side length, only non-negative values are physically meaningful because a length cannot be negative.

4. Therefore, while there are two solutions to the equation, only $$ s = 10 $$ is valid when representing the side length of a square.
There are two solutions to the equation $$ s^2 = 100 $$: $$ s = 10 $$ and $$ s = -10 $$. However, since a square's side length cannot be negative, only $$ s = 10 $$ is valid.

Each side of the square measures Convince Me! Why are there two possible solutions to the equation \( s^{2}=100 \) ? Explain why only one of the solutions is valid in this situation.

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