1. The problem is to simplify or understand the expression $\sqrt{x} \sum_{i=1}^n i^2$. 2. Recall the formula for the sum of squares: $$\sum_{i=1}^n i^2 = \frac{n(n+1)(2n+1)}{6}$$. 3. Substitute this formula into the expression: $$\sqrt{x} \cdot \frac{n(n+1)(2n+1)}{6}$$. 4. This means the expression equals $$\frac{\sqrt{x} \cdot n(n+1)(2n+1)}{6}$$. 5. This is the simplified form, showing the product of $\sqrt{x}$ and the sum of squares from 1 to $n$. 6. To evaluate for specific values of $x$ and $n$, plug them into this formula.