K2-291b: A rocky super-Earth in a 2.2 day orbit

K2-291 (EPIC 247418783) is a solar-type star with a radius of R_star = 0.899 $\pm$ 0.034 R_sun and mass of M_star=0.934 $\pm$ 0.038 M_sun. From K2 C13 data, we found one super-Earth planet (R_p = 1.589+0.095-0.072 R_Earth) transiting this star on a short period orbit (P = 2.225177 +6.6e-5 -6.8e-5 days). We followed this system up with adaptive-optic imaging and spectroscopy to derive stellar parameters, search for stellar companions, and determine a planet mass. From our 75 radial velocity measurements using HIRES on Keck I and HARPS-N on Telescopio Nazionale Galileo, we constrained the mass of EPIC 247418783b to M_p = 6.49 $\pm$ 1.16 M_Earth. We found it necessary to model correlated stellar activity radial velocity signals with a Gaussian process in order to more accurately model the effect of stellar noise on our data; the addition of the Gaussian process also improved the precision of this mass measurement. With a bulk density of 8.84+2.50-2.03 g cm-3, the planet is consistent with an Earth-like rock/iron composition and no substantial gaseous envelope. Such an envelope, if it existed in the past, was likely eroded away by photo-evaporation during the first billion years of the star's lifetime.