1. **State the problem:** Simplify the expression $x^2 - \sqrt{x}$. 2. **Recall the definitions:** - $x^2$ means $x$ multiplied by itself. - $\sqrt{x}$ means the square root of $x$, which is the same as $x^{\frac{1}{2}}$. 3. **Rewrite the expression using exponents:** $$x^2 - x^{\frac{1}{2}}$$ 4. **Check for common factors:** Both terms have a factor of $x^{\frac{1}{2}}$ because $x^2 = x^{\frac{1}{2} + \frac{3}{2}}$. 5. **Factor out the common term $x^{\frac{1}{2}}$:** $$x^2 - x^{\frac{1}{2}} = x^{\frac{1}{2}} \left( x^{\frac{3}{2}} - 1 \right)$$ 6. **Rewrite the factored form:** $$\boxed{x^{\frac{1}{2}} \left( x^{\frac{3}{2}} - 1 \right)}$$ This is the simplified form showing the common factor. **Note:** This expression cannot be simplified further unless specific values of $x$ are given or additional operations are requested.