Define the relationship

The mean proportional $M$ between two numbers $a$ and $b$ is given by $M = \sqrt{a \times b}$.

$M = \sqrt{a \times b}$

Substitute given values

Given $M = 72$, $a = 18$, and the second number is $y$, we set up the equation $72 = \sqrt{18 \times y}$.

$72 = \sqrt{18 \times y}$

Solve for y

Square both sides to eliminate the square root: $72^2 = 18 \times y$. Then calculate $y = \frac{5184}{18} = 288$.

$y = \frac{72 \times 72}{18} = 288$