Question 1105180
If a, b, and c are positive numbers such that √a/√b = 8c and ac = b,
 what is the value of c?
{{{sqrt(a)/sqrt(b)}}} = 8c
we can write it
 {{{sqrt(a/b)}}} = 8c
square both sides
{{{a/b = 64c^2}}}
a = {{{64bc^2}}}
b = {{{a/(64c^2)}}}
we know ac = b 
ac = {{{a/(64c^2)}}}
divide both sides by a
c = {{{1/(64c^2)}}}
multiply both sides by c^2 
{{{c^3 = 1/64}}}
find the cube root of both sides
c = {{{1/4}}}