If √(y/169) = 54/39 (i.e., 18/13), find the value of y.

Introduction / Context:This is a straightforward radical equation where the square root of a fraction equals a given rational number. Squaring both sides clears the square root and yields a simple linear equation in y.

Given Data / Assumptions:√(y/169) = 54/39 = 18/13.

Concept / Approach:Square both sides carefully: (√(y/169))^2 = (18/13)^2 ⇒ y/169 = 324/169. Then multiply both sides by 169 to isolate y.

Step-by-Step Solution:

Verification / Alternative check:Substitute back: √(324/169) = √324/√169 = 18/13 = 54/39. Checks out.

Why Other Options Are Wrong:108 and 169 square-root to different ratios; 2916 and 4800 are overestimates not matching the given equality.

Common Pitfalls:Squaring only the numerator or denominator, or failing to simplify 54/39 to 18/13 first (though not required, it makes the check clearer).

Final Answer:324