Least Number to Add to 1901 to Make a Perfect Square

Step 1: Understand the Problem

A perfect square is a number like 1, 4, 9, 16, 25, 36, … (i.e., n² for some integer n).

We need a number x such that:

1901 + x = n²

where n is an integer, and x is as small as possible.

Step 2: Find the Nearest Perfect Square

Estimate n by taking the square root of 1901:

√1901 ≈ 43.6

Nearest integers: 43 and 44

• 43² = 1849 → too small
• 44² = 1936 → just above 1901 

Step 3: Find the Number to Add

x = 1936 − 1901 = 35

The least number to add is: 35