Find the mean proportional of 144 and 9.

The correct option is 36.

Understanding Mean Proportional:
The mean proportional (or geometric mean) between two positive numbers $a$ and $b$ is a number $x$ such that:

$\frac{a}{x}=\frac{x}{b}$

Cross-multiplying gives:

$x^2=a\×b$

Taking the square root of both sides:

$x=\sqrt{a\×b}$

Step-by-Step Calculation:
Given the two numbers:

$a=144$

$b=9$

Substitute these values into the mean proportional formula:

$x=\sqrt{144\×9}$

We can evaluate the square root by taking the square roots of the individual factors:

$x=\sqrt{144}\×\sqrt{9}$

Since $\sqrt{144}=12$ and $\sqrt{9}=3$:

$x=12\×3$

$x=36$

Thus, the mean proportional of 144 and 9 is 36.