Work backwards from the pressure amplitude to the level.
Intensity scales as the square of pressure amplitude, $I\propto p_0^2$. So in decibels
\[\beta=10\log_{10}\frac{I}{I_0}=20\log_{10}\frac{p_0}{p_{0,\text{ref}}}\]
The rise in level is
\[\Delta\beta=20\log_{10}\frac{p_{0,2}}{p_{0,1}}=10\ \text{dB}\]
Solving,
\[\log_{10}\frac{p_{0,2}}{p_{0,1}}=\tfrac{10}{20}=\tfrac12\quad\Rightarrow\quad\frac{p_{0,2}}{p_{0,1}}=10^{1/2}=\sqrt{10}\]
So the pressure amplitude grows by a factor $\sqrt{10}$ (about $3.16$).
\[\boxed{\sqrt{10}}\]