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when you square a negative number does it become positive ?

**Squaring a Negative Number: A Comprehensive Explanation**

When you square a negative number, the result is positive. This occurs because squaring a number involves multiplying the number by itself. Here’s a detailed breakdown:

1. **Definition of Squaring**: Squaring a number means multiplying the number by itself. For example, squaring -3 is (-3) × (-3).

2. **Multiplication of Negatives**: The product of two negative numbers is positive. Therefore, (-3) × (-3) equals 9, a positive number.

3. **Parentheses and Order of Operations**: The placement of parentheses affects the outcome.
– With parentheses: (-3)^2 = 9.
– Without parentheses: -3^2 = -(3^2) = -9.

4. **Exponentiation Precedence**: In the absence of parentheses, exponents are applied before the negative sign. Thus, -3^2 is interpreted as -(3^2) = -9.

5. **Graphical Representation**: The graph of y = x^2 is a parabola opening upwards, showing that both positive and negative x-values yield positive y-values.

6. **Special Case of Zero**: Squaring zero results in zero, which is neither positive nor negative.

7. **Applications**: Understanding this concept is crucial in algebra, calculus, and physics, where signs and operations affect outcomes.

In conclusion, squaring a negative number typically results in a positive number, emphasizing the importance of parentheses and operator precedence in mathematical expressions.