A star with a brightness of 100,000 suns and a surface temperature of about 3,000 K would be classified as a Red Supergiant on the Hertzsprung-Russell diagram, given its high luminosity and low temperature.
To classify a star on the Hertzsprung-Russell diagram with a brightness of 100,000 suns and a surface temperature of about 3,000 degrees Kelvin (K), find a spot on the diagram that correlates to these two parameters.
Since the given luminosity is very high while the temperature is relatively low, it implies that the star cannot be on the main sequence, which is characterized by a correlation between higher masses, luminosities, and temperatures.
Instead, a star with such a high luminosity but a low temperature would fall into the category of a red supergiant.
Red Supergiants are located in the upper right portion of the H-R diagram, which is consistent with the characteristics of being very bright (high luminosity) but cool in terms of surface temperature (low temperature relative to other stars with similar brightness).