If $A$, $B$ and $C$ are positive integers such that $\frac{A\sqrt{B}}{C} = \frac{8}{3\sqrt{2}}$, what is the value of $A+B+C$ given that $A$ and $C$ have no common prime factors, and $B$ has no perfect-square factors other than 1?
+128460 \($\frac{A\sqrt{B}}{C} = \frac{8}{3\sqrt{2}}$\)
Implies that
A√B / C = 8 / √18 cross-muliply
A√[18B] = 8C ..... let B = 2.....and we have
A√36 = 8C
6A = 8C ......this is equalized when A = 4 and C = 3
Check :
4√2 / 3 = 8 / [ 3 √2]
4 √2 = 8 / √2
√2 * √2 = 8 / 4
2 = 2
So A + B + C = 4 + 3 + 2 = 9
