If $\sqrt{18 \times 14 \times x} = 84$, then $x$ equals

Concept & Logic Square both sides of the radical equation to remove the square root, then isolate the unknown variable by dividing. Avoid full multiplication early on to make simplification easier through cancellation. Step-by-Step Solution * **Given:** $\sqrt{18 \times 14 \times x} = 84$ * **Calculation:** Square both sides to eliminate the radical: $18 \times 14 \times x = 84^2$ $18 \times 14 \times x = 84 \times 84$ * Isolate $x$ by dividing both sides by $(18 \times 14)$: $x = \frac{84 \times 84}{18 \times 14}$ * Simplify the fraction by cancelling out common factors. First, note that $84 \div 14 = 6$: $x = \frac{6 \times 84}{18}$ * Simplify further. Notice that $18 \div 6 = 3$: $x = \frac{84}{3}$ * Complete the final division: $x = 28$ Exam Strategy & Shortcut Keep everything factored. When you see $18 \times 14 \times x = 84 \times 84$, immediately scan for multiples. $14 \times 6 = 84$. That leaves $18 \times x = 6 \times 84$. Divide $18$ by $6$ to get $3x = 84$. Therefore, $x = 28$. This completely avoids any large arithmetic. Common Pitfall Squaring $84$ to get $7056$ and multiplying $18 \times 14$ to get $252$, and then attempting to divide $7056 \div 252$ manually, which is highly prone to calculation errors and wastes precious time. Final Answer **Therefore, the correct answer is 28.**