A negative number squared is always ....a negative number.a positive number.Not real.a irrational number.

Break Down the Problem

1. Identify the operation: squaring a negative number.
2. Analyze the properties of squaring.

Relevant Concepts

1. The definition of a negative number.
2. The mathematical property of squaring a number:
   • For any real number $x$, $x^2 \geq 0$.

Analysis and Detail

1. Let $x$ be a negative number, so $x < 0$.
2. When squaring $x$: $x^2 = (-a)^2 = a^2 \quad \text{(where \( a > 0 \))}$
3. Since squaring a negative number results in a positive number, we conclude: $x^2 > 0$

Verify and Summarize

We established that squaring any real number, negative or positive, yields a non-negative result. Specifically, squaring a negative number results in a positive number.

Final Answer

A negative number squared is always a positive number.