The red dot on the number line below represents the square root of an integer. explain how to determine this integer, and then find it. the red dot is located between 12 and 13. the red dot is about half way between 12 and 13, but a little below the half way point, so the red dot represents a little below half way between the two square roots. since the square root of 144 is equal to 12 and the square root of 169 is equal to 13, then the red dot is located between the two square roots. by extension, to the nearest integer, the approximate value of the dot will be a little below half way between and , which is about the square root of .