1. Speed of light in a medium

The speed of light in a medium is

$v=\frac{1}{\sqrt{\mu\epsilon}}$

where

$\mu=\mu_r\mu_0, \qquad \epsilon=\epsilon_r\epsilon_0$

So,

$v=\frac{1}{\sqrt{\mu_r\mu_0\,\epsilon_r\epsilon_0}}$

But in vacuum,

$c=\frac{1}{\sqrt{\mu_0\epsilon_0}}$

Hence,

$v=\frac{c}{\sqrt{\mu_r\epsilon_r}}$

Therefore, the factor by which the speed in vacuum is greater than that in the medium is

$\frac{c}{v}=\sqrt{\mu_r\epsilon_r}$

2. Substitute the given values

Given:

$\mu_r=\frac{10}{\pi}, \qquad \epsilon_r=\frac{1}{0.0885}$

Thus,

$\frac{c}{v}=\sqrt{\frac{10}{\pi}\cdot \frac{1}{0.0885}}$

Now use

$\pi \approx 3.14$

Then,

$\frac{10}{\pi}\approx \frac{10}{3.14}\approx 3.1847$

and

$\frac{1}{0.0885}\approx 11.2994$

So,

$\mu_r\epsilon_r \approx 3.1847 \times 11.2994 \approx 35.99 \approx 36$

Hence,

$\frac{c}{v}=\sqrt{36}=6$

3. Final answer

The velocity of light in vacuum is greater than that in the medium by

$\boxed{6}$

times.

4. Comparison with stored answer

Stored correct answer = $6$

Our derived answer = $6$

So the derived answer agrees with the stored correct answer.