Question

Find the mean proportional between 0.06 and 0.96.

Answer 1

Let the required mean proportional be x.
So, 0.06, x, and 0.96 are in continued proportion.
So, $0.06:x::x:0.96$
In a continued proportion, the product of the extremes is equal to the square of the third proportional.
So, $x^2=0.06\times 0.96$
$x=\sqrt{0.06\times 0.96}=\sqrt{0.0576}=0.24$