If two charges q _ 1 and q _ 2 are separated with distance d and...

The force between the two charges when they are placed in dielectric is

${F}_{1} = \dfrac{1}{4\pi{ε}_{o}k}\dfrac{{q}_{1}{q}_{2}}{{d}^{2}}$

The force between the two charges when they are placed at separation $d '$ is

${F}_{2} = \dfrac{1}{4\pi{ε}_{o}}\dfrac{{q}_{1}{q}_{2}}{d{'}^{2}}$

Since, the force between the two charges is same in both case

${F}_{1} = {F}_{2}$

$⇒ \dfrac{1}{4\pi{ε}_{o}k}\dfrac{{q}_{1}{q}_{2}}{{d}^{2}} = \dfrac{1}{4\pi{ε}_{o}}\dfrac{{q}_{1}{q}_{2}}{d{'}^{2}}$

$⇒ d ' = d\sqrt{k}$