Question

Find the mean proportional of 1 and 1/9.

Answer 1

Answer:

There are various uses of the square root, one of which is to find a mean proportional between any two numbers, which is performed thus: Multiply the two given numbers together, then extract the square root out of their product, and it will be the mean proportional sought.

Answer 2

Answer:

Let y be the mean proportion between 1 and 1/9.

it means

$1,y,y, \frac{1}{9} are \: in \: proportion \\ so \: \frac{1}{y} = \frac{y}{ \frac{1}{9} } \\ {y}^{2} = \frac{1}{9} \\ y = \sqrt{ \frac{1}{9} } \\ y = \frac{1}{3}$