Question

if a star is very cool, but very bright, it must be:
the hertzsprung - russell diagram
blue super giant
white dwarf
red super giant
main sequence

Explanation:

Step1: Recall HR Diagram Axes

The Hertzsprung - Russell (HR) diagram has temperature (decreasing to the right, so cooler stars are on the right) on the x - axis and absolute magnitude (brightness, increasing upward) on the y - axis.

Step2: Analyze Star Properties

A cool star (low temperature, so right - hand side of the HR diagram) and very bright (high absolute magnitude, so upper part of the HR diagram) falls in the region of red super giants. Blue super giants are hot (left - hand side) and bright. White dwarfs are dim (low absolute magnitude) and hot/cool (but dim). Main sequence stars follow a diagonal; cool main sequence stars are dim.

Answer:

red super giant