Question

Find the mean proportional of the following:

`1/16, 4/25`

Answer 1

Let x be the mean proportional between `1/16 and 4/25`.

Then,

`1/16` : x :: x, `4/25`

⇒ `(1/16)/x = x/(4/25)`

⇒ x² = `1/16 xx 4/25`

⇒ x = ±`sqrt(1/6 xx 4/25)`

⇒ x = ±`sqrt(4/400)`

⇒ x = ±`sqrt(1/100)`

⇒ x = ±`1/10`

As `-1/10` does not lie between two positive numbers `1/16 and 4/25`.

∴ x = `1/10`