Question

How many integers between 1 and 10000 are neither squares nor cubes?

a) 2896
b) 5475
c) 7321
d) 9002

Answer 1

The correct count of integers between 1 and 10000 that are neither squares nor cubes is 5475 (Option B).

Step-by-step explanation:

Determine the number of integers that are perfect squares between 1 and 10000. The square root of 10000 is 100, so there are 100 squares.

Determine the number of integers that are perfect cubes between 1 and 10000. The cube root of 10000 is approximately 21.5, so there are 21 cubes.

Subtract the counts of squares and cubes from the total number of integers between 1 and 10000: 10000 - 100 - 21 = 5479.

However, the number 1 is counted twice (as both a square and a cube), so subtract 1 from the result: 5479 - 1 = 5478.

Therefore, the correct count is 5475 integers, corresponding to Option B.