Which of the following cannot be the square of a natural number?

Given data & approach

• Check each option against properties of perfect squares.

Checks

1936 = 44^2 ✔2209 = 47^2 ✔2401 = 49^2 ✔1537 ends with 7. No perfect square in base-10 ends with 2, 3, 7 or 8 ⇒ cannot be a perfect square.

Additional note

Also, √1537 ≈ 39.2; 39^2 = 1521 and 40^2 = 1600, neither equals 1537.

Final Answer

Number that cannot be a square: 1537.