Question

Find the mean proportional of the following pairs:

(1) 8, 18
(2) 8, 32
(3) ak and ak³

Answer 1

(1)

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{mean}\mathrm{proportional}\mathrm{be}x. \\ \therefore x^2=8\times 18 \\ \Rightarrow x^2=144 \\ \Rightarrow x=12 \end{gathered}$$

(2)

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{mean}\mathrm{proportional}\mathrm{be}x. \\ \therefore x^2=8\times 32 \\ \Rightarrow x^2=256 \\ \Rightarrow x=16 \end{gathered}$$

(3)

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{mean}\mathrm{proportional}\mathrm{be}x. \\ \therefore x^2=ak\times a{k}^3 \\ \Rightarrow x^2=a^2{k}^4 \\ \Rightarrow x=a{k}^2 \end{gathered}$$