Equilibrium constant reaction problem

[ahoy hoy]

Homework Statement

Given the equilibrium,
A2(g) + 4C(g) 2AC2(g), K1 = 4.8

It follows that, for the reaction,
AC2(g) A2(g) + 2C(g), K2 = X

X would be

Homework Equations

The Attempt at a Solution

Since the equation is the inverse, i know to use 1/K1.
The mole ratio of everything is halved- why does this mean taking the square root of K1, considering the solution to x is 1/(sqrt4.8).
I woulda just gone for the other multiple choice option 1/2.4

 

[Vagrant]

yeah you have to take sq root of the inverse.

 

[ahoy hoy]

but why...could u relate it to theory?

 

[Vagrant]

write the expression for eq const for reaction 1 and 2 and subtitute k2 in the exp for k1