Question

Find the mean proportional between 7 by 11 and 9 by 308

Answer 1

What is the mean proportional of 7\11 and 9\308?

Let x be the mean proportional. Then

(711)x=x(9308).

Cross-multiply to get

x×x=711×9308

=633388.

Use prime factorisations because of the size of the denominator:

x2=7×3222×7×112

=77×3222×112

=3222×112.

Then taking the positive square root of the right-hand side because the given fractions are positive, get that

x2−−√=3222×112−−−−−−−√,

x=32−−√22×112−−−−−−−√  

=32−−√22−−√×112−−−√

=32×11=322.

∴ the mean proportional is

322.

Answer 2

Answer:

The answer is

$\frac{3}{22}$