The mean proportional between 4 and 9 is:

The mean proportional (also known as the geometric mean) between two numbers $a$ and $b$ is a value $x$ such that the ratio $a:x$ is equal to the ratio $x:b$. 1. **Identify the formula:** The relationship is expressed as $\frac{a}{x} = \frac{x}{b}$, which simplifies to: $$x^2 = a \times b$$ $$x = \sqrt{a \times b}$$ 2. **Substitute the given values:** We are given $a = 4$ and $b = 9$. $$x = \sqrt{4 \times 9}$$ 3. **Calculate the product:** $$x = \sqrt{36}$$ 4. **Find the square root:** $$x = 6$$ Therefore, the mean proportional between 4 and 9 is **6**.