Which one of the following cannot be the square of a natural number?
2023
Which one of the following cannot be the square of a natural number?
Answer: C. 42437 — ConceptA natural number is a perfect square when it can be written as n × n for some natural number n. Squares have restricted final digits, and neighboring…
- A.
32761
- B.
81225
- C.
42437
- D.
More than one of the above
- E.
None of the above
Show answer & explanation
Correct answer: C
Concept
A natural number is a perfect square when it can be written as n × n for some natural number n.
Squares have restricted final digits, and neighboring integer squares provide an independent way to test a candidate.
Application
For 32761, 181 × 181 = 32761, so 32761 is a natural-number square.
For 81225, 285 × 285 = 81225, so 81225 is a natural-number square.
The last two digits 37 cannot occur in a perfect square; hence 42437 cannot be a natural-number square.
Cross-check
The consecutive squares around 42437 are 2062 = 42436 and 2072 = 42849. Because 42437 lies strictly between them, it is not a perfect square.
Therefore, 42437 is the required value.