Given the relation \(y = k\sqrt{x}\), we can find the value of \(k\) using the first pair of \(x\) and \(y\) values from the table:

\(0.5 = k\sqrt{1}\)

Solving for \(k\), we get \(k = 0.5\).

Now, we can use this value of \(k\) to find the value of \(p\) that makes the third \(y\) value in the table (2.5) satisfy the relation:

\(2.5 = 0.5\sqrt{p}\)

Solving for \(p\), we get \(p = \left(\frac{2.5}{0.5}\right)^2 = 25\).