The least number to be added to make 269 a perfect square is

Concept

A perfect square is the square of an integer. To find the least number that must be added to a given integer N to make it a perfect square, locate the smallest perfect square greater than N; the required addition equals that perfect square minus N.

Application

1. Estimate the square root of 269: since 162 = 256 and 172 = 289, the number 269 lies between these two squares, so √269 ≈ 16.4.

2. The next perfect square greater than 269 is therefore 289, since 172 = 289.

3. The least number to be added is 289 − 269 = 20.

Cross-check

Check: 269 + 20 = 289 = 172, confirming the result. Also, 162 = 256 is less than 269, so no smaller addition can work — 20 is indeed the least number needed.