If y varies directly as the square root of x, then we can write the relationship between y and x as \(y = k \sqrt{x}\), where k is the constant of variation.

We can use the given information that y = 3 when x = 16 to find the value of k. Substituting these values into the equation, we get:

\(3 = k \sqrt{16}\), which simplifies to:

\(k = \frac{3}{4}\).

Now that we know the value of k, we can use the equation \(y = k \sqrt{x}\) to find the value of y when x = 64.

Substituting these values into the equation, we get:

\(y = \frac{3}{4} \sqrt{64} = \frac{3}{4} \times 8 = 6\).

Therefore, when x = 64, y is equal to 6.