First, let's write the expression described by the problem.
![y=\frac{k(ab)}{\sqrt[]{c}}](https://img.qammunity.org/2023/formulas/mathematics/college/wpn8dlea0bl0r61zaa8ayo4dqy6ffa0lik.png)
Then, we use the given magnitudes to find k (the constant of proportionality).
![\begin{gathered} 14=\frac{k(5\cdot2)}{\sqrt[]{25}} \\ 14=(10k)/(5) \\ 14=2k \\ k=(14)/(2) \\ k=7 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/zxamkalkbhkmjuuy979aqpx0lgj42ckoso.png)
The constant of proportionality is 7.
Then, we use k value to find y with a = 4, b = 4, and c = 4.
![\begin{gathered} y=\frac{7(4\cdot4)}{\sqrt[]{4}}=(112)/(2) \\ y=56 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/cgd1ehxlgl3i8qqr2ooi0j3f6ejtcbppar.png)
Therefore, the value of y is 56.