1. **State the problem:** Simplify or analyze the expression $x^2 - \sqrt{x}$. 2. **Recall the definitions:** $x^2$ means $x$ multiplied by itself, and $\sqrt{x}$ means the square root of $x$, which is the number that when squared gives $x$. 3. **Rewrite the square root:** $\sqrt{x} = x^{\frac{1}{2}}$. So the expression becomes $x^2 - x^{\frac{1}{2}}$. 4. **Check for common factors:** There is no common factor between $x^2$ and $x^{\frac{1}{2}}$ that can be factored out easily because their exponents differ. 5. **Interpretation:** The expression is already simplified as a difference of two terms with different powers of $x$. 6. **Domain consideration:** Since $\sqrt{x}$ is defined only for $x \geq 0$, the domain of the expression is $x \geq 0$. 7. **Final expression:** $x^2 - \sqrt{x}$ or equivalently $x^2 - x^{\frac{1}{2}}$.