At 298K , the equilibrium constant is 2 × 10 ^ 15 for the reaction:...

$Cu\left(s\right) + 2{Ag}^{+}\left(aq\right) ⇌ {Cu}^{2 +}\left(aq\right) + 2Ag\left(s\right); {K}_{eq} = 2 \times {10}^{15}$

$\dfrac{1}{2}{Cu}^{2 +}\left(aq\right) + Ag\left(s\right) ⇌ \dfrac{1}{2}Cu\left(s\right) + {Ag}^{+}\left(aq\right)$

The equilibrium reaction is reversed and multiplied with $\dfrac{1}{2}$,

Hence, ${K}_{eq}^{'} = \dfrac{1}{\sqrt{{K}_{eq}}} = \dfrac{1}{\sqrt{2 \times {10}^{15}}} = x \times {10}^{- 8}$

$⇒ \dfrac{1}{\sqrt{20}} \times \dfrac{1}{{10}^{7}} = x \times {10}^{- 8}$

$⇒ \dfrac{1}{\sqrt{20}} \times {10}^{- 7} = x \times {10}^{- 8}$

$\dfrac{10}{\sqrt{20}} = x$

$⇒ x = \dfrac{\sqrt{10}}{\sqrt{2}} = \sqrt{5} = 2 . 236$

$≃ 2 . 24$