Question

________ is the general formula to find the number of non-square numbers in between two consecutive squares.

(a) n^2+2n-1

(b) n^2-1

(c) 2n+1

(d) n+1

I have been asked this question during an interview for a job.

The above asked question is from Patterns in Squares topic in section Squares and Square Roots of Mathematics – Class 8

Answer 1

Correct answer is (c) 2n+1

Easiest explanation: If we want to find the general formula for the number of non-square numbers in between two consecutive squares, we assume to the natural numbers to be n & n+1

We square and subtract the smaller from the greater number,

(n+1)^2-n^2=(n^2+2n+1)-n^2=2n+1