Question

how many positive integers between 100 and 1100 that are neither a square nor a cube of a positive integers​

Answer 1

Step-by-step explanation:

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Answer 2

Given: Integers between 100 and 1100.

To find: How many positive integers between 100 and 1100 that are neither a square nor a cube of a positive integers​.

Solution: 70 positive integers between 100 and 1100 are neither a square nor a cube of a positive integers​.

There are a total of 999 integers between 100 and 1100. The numbers whose squares lie between 100 and 1100 range from 11 (121) to 33 (1089). There are 23 numbers from 11 to 33.

Now, the numbers whose squares lie between 100 and 1100 range from 5 (125) to 10 (1000). There are 6 numbers from 5 to 10. Thus, the total number of positive integers between 100 and 1100 that are square or a cube of a positive integers​ is

$23 + 6 = 29$

Hence, the number of integers that are neither square nor a cube of a positive integers​ is

$99-29 = 70$

Therefore, 70 positive integers between 100 and 1100 are neither a square nor a cube of a positive integers​.