Answer
$\sqrt{3}$
Work Step by Step
Consider the ideal gas law, PV=nRT. If the volume and the amount of gas do not change, and the pressure is tripled, the absolute temperature also triples.
The rms speed is given by equation 13–9. We see that the rms speed is proportional to the square root of the absolute temperature, so the rms speed is multiplied by a factor of $\sqrt{3}\approx1.73$.