.

To simplify the expression \((14\sqrt{3})^2\), follow these steps:

1. Square the coefficient: \(14^2 = 196\).
2. Square the square root: \((\sqrt{3})^2 = 3\).

Now multiply the results: \[196 \times 3 = 588\]

So, \((14\sqrt{3})^2 = 588\).