Question

Find the mean proportional between $\text{4 and 16}$.

Answer 1

Explanation:

Let the mean proportional between $\text{4 and 16}$ is $\text{a}$, it means,

$\text{4:a::a:16}$ becomes in proportion.

We know that, $\text{Product of extremes terms = Product of means terms}$

$$\begin{gathered} \Rightarrow a\times a=4\times 16 \\ \Rightarrow a^2=4\times 16 \\ \Rightarrow a=\sqrt{4\times 16} \\ \Rightarrow a=2\times 4 \\ \Rightarrow a=8 \end{gathered}$$

Hence, the mean proportional between $\text{4 and 16}$ is $8$.