If b varies directly as the square root of a, and b=2 when a=9, find the equation connecting b and a.

If $b$ varies directly as the square root of $a$, we can write this relationship as:

$$b = k\sqrt{a}$$

where $k$ is the constant of proportionality.

We are given that $b=2$ when $a=9$. Substitute these values into the equation:

$$2 = k\sqrt{9}$$ $$2 = k \cdot 3$$

Divide both sides by 3:

$$k = \frac{2}{3}$$

Substitute the value of $k$ back into the direct variation equation:

$$b = \frac{2}{3}\sqrt{a}$$

The correct option is [C] $b = \frac{2}{3}\sqrt{a}$.