Final answer:
The number of integers between 25 to 250 that are not perfect cubes is 221, calculated by taking the total amount of integers in the range (226) and subtracting the number of perfect cubes within that range (5).
Step-by-step explanation:
To identify the number of integers in the list from 25 to 250 that are not perfect cubes, we first list all the perfect cubes within this range. A perfect cube is a number that can be expressed as the cube of an integer.
The perfect cubes between 25 to 250 are:
23 = 8 (which is below 25 so we do not consider this)
33 = 27
43 = 64
53 = 125
63 = 216
Those are the only integers within the range of 25 to 250 that are perfect cubes. Now, to count the integers that are not perfect cubes, we count all the integers in the range and then subtract the number of perfect cubes.
The range from 25 to 250 has (250 - 25) + 1 = 226 total integers. There are 5 perfect cubes as we listed. Therefore, the number of integers that are not perfect cubes is:
226 total integers - 5 perfect cubes = 221 integers that are not perfect cubes.
Although the options provided in the question (10, 15, 20, 25) do not include the correct answer, which is 221, the best approach is to calculate as we have done to arrive at the correct answer.