In the equation $\frac{4050}{\sqrt{x}} = 450$, the value of $x$ is

### Concept & Strategy Rearrange the fractional statement to bring the variable radical expression to one side, simplify the integers, and square the remaining value. Algebraic property: $$ \text{If } \frac{a}{\sqrt{x}} = b, \text{ then } \sqrt{x} = \frac{a}{b} $$ ### Step-by-Step Solution - **Step 1: Rearrange the algebraic fraction.** - $\frac{4050}{450} = \sqrt{x}$ - **Step 2: Simplify the division balance.** - Cancel out the common zeros: $\frac{405}{45} = \sqrt{x}$ - Dividing $405$ by $45$: $\sqrt{x} = 9$ (since $45 \times 10 = 450$, then $450 - 45 = 405$). - **Step 3: Square both sides.** - $x = 9^2 = 81$ ### Exam Strategy & Shortcut Directly observe the ratio relationship. $450$ goes into $4050$ exactly $9$ times. Therefore, $\sqrt{x}$ equals $9$. The square of $9$ is $81$. This can easily be checked in under 5 seconds. ### Common Pitfall Selecting option (a) $9$ by accident because of a lack of attention to the radical sign over the variable $x$. Always check whether the question requires $x$ or $\sqrt{x}$. ### Final Answer Therefore, the correct answer is 81.