IMC 2015 Q5
5. Which of the following numbers is not a square?
- A \(1^6\)
- B \(2^5\)
- C \(3^4\)
- D \(4^3\)
- E \(5^2\)
Intermediate Mathematical Challenge 2015, Question 5. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B \(2^5\)
\(1^6 = (1^3)^2\), \(3^4 = (3^2)^2\), \(4^3 = 64 = 8^2\) and \(5^2\) are all squares. However, \(2^5 = 32\) and is not a square.
Solution © UK Mathematics Trust, from the IMC 2015 solutions. Longer versions with investigations: Solutions and investigations (PDF).