Question

Jonathan likes the first $100$ natural numbers (which are the numbers $1$, $2$, $3$, and so on up until and including $100$). he decides to go through them one by one, and each time he finds a number that is a perfect square or a perfect cube, he gets very happy and screams "woot!". how many times did jonathan scream "woot!"?

Answer 1

Jonathan will scream "woot!" 50 times.

Step-by-step explanation:

The first 100 natural numbers are 1, 2, 3, ..., 100.

A perfect square is a number that can be expressed as the square of an integer. For example, 4, 9, and 16 are perfect squares because they can be expressed as 2², 3², and 4² respectively.

A perfect cube is a number that can be expressed as the cube of an integer. For example, 8, 27, and 64 are perfect cubes because they can be expressed as 2³, 3³, and 4³ respectively.

To find the numbers that are either perfect squares or perfect cubes, we need to count the numbers that are multiples of 2 (excluding those multiples that are also multiples of 3). There are 50 natural numbers that are multiples of 2.

Therefore, Jonathan will scream "woot!" 50 times.