If x is the least number which must be added to 955 to make it a perfect…

The least number that must be added to a number N to make it a perfect square equals the gap between N and the smallest perfect square that is not less than N: if m is the smallest whole number with m2 ≥ N, the required number is x = m2 − N.

1. 302 = 900 and 312 = 961 are the perfect squares immediately below and above 955.

2. Since 900 < 955 < 961, the smallest perfect square not less than 955 is 961.

3. The least number to add is x = 961 − 955 = 6.

4. Therefore 3x + 2 = 3 × 6 + 2 = 18 + 2 = 20.

Adding 6 to 955 gives 961, and 31 × 31 = 961 confirms this is indeed a perfect square; no smaller addition can work because 955 already lies above 900 = 302, the preceding perfect square.