If y varies directly as \(\sqrt{n}\), then we can write the relationship between y and n as y = k\(\sqrt{n}\), where k is the constant of variation. We can find the value of k by using the information that y = 4 when n = 4:

\(4 = k\sqrt{4}\)

\(k = \frac{4}{2} = 2\)

Now that we know the value of k, we can use it to find the value of y when n = 1\(\frac{7}{9}\):

\(y = 2\sqrt{1\frac{7}{9}}\)

\(y = 2\sqrt{\frac{16}{9}}\)

\(y = 2 \times \frac{4}{3}\)

\(y = \frac{8}{3}\)

So, when n = 1\(\frac{7}{9}\), y is equal to \(\frac{8}{3}\).