How to find number of perfect squares in first 1000 natural numbers
Answers
Assuming we are only dealing with whole integers and ignoring all else. Every whole integer can create a square number.
1 square = 1
2 square = 4
3 square = 9 etc.
So starting from 1 we can find our upper boundary by finding the numbers that are around the 1000 limit.
We know 302=900so that is going to be close. We can make the squares of the next few integers.
31 square = 961
32 square = 1024
32 square is too big. Therefore there are 31 square numbers between 1–1000 assuming we are only dealing with whole positive integers. There are a lot of assumptions that I am making in this answer. For one, I am assuming that we are only worried about whole numbers as any decimal or fraction of a number can create a square number and this would create infinite solutions. I am also assuming that we are only worried about the square numbers themselves and not considering a squared positive and squared negative to be different things.
Depending on the questions these assumptions may or may not be correct.