The quantities P, Q and R are such that P varies directly as Q and inversely as the square root of R. when P=8, Q=10 and R=16. Determine the equation connecting P, Q and R.

The problem states that P varies directly as Q and inversely as the square root of R. This can be written as:

$$P = \frac{kQ}{\sqrt{R}}$$

where $k$ is the constant of proportionality.

We are given the values $P = 8$, $Q = 10$, and $R = 16$. Substitute these values into the equation:

$$8 = \frac{k \cdot 10}{\sqrt{16}}$$ $$8 = \frac{10k}{4}$$ $$8 = 2.5k$$

Divide both sides by 2.5 to solve for $k$:

$$k = \frac{8}{2.5}$$ $$k = 3.2$$

Substitute the calculated value of $k = 3.2$ back into the general variation equation:

$$P = \frac{3.2Q}{\sqrt{R}}$$

The equation connecting P, Q, and R is P = 3.2Q / √R.