Find x such that both occurrences of x in the equation x = (√162 × √128) / x are equal.

Problem restatementDetermine the common value of x that satisfies x = (√162 × √128) / x.

Given data

• Equation: x = (√162 × √128) / x

Concept/ApproachUse √a × √b = √(ab). Multiply both sides by x to obtain a quadratic in x.

Step-by-step calculationx = √162 × √128 / x = √(162 × 128) / xx² = √(20736) = 144x = √144 = 12 (taking the positive principal value)

Verification/AlternativeCheck: √162 × √128 = √20736 = 144; then (144) / 12 = 12, which equals x.

Common pitfallsForgetting to combine radicals or missing that x appears in denominator; also note that in typical aptitude contexts, the positive root is expected.

Final Answer12