Question

Which among \( 2^{1/2}, 3^{1/3}, 4^{1/4}, 6^{1/6} \) and \( 12^{1/12} \) is the largest?

• A. \( 2^{1/2} \)
• B. \( 3^{1/3} \)
• C. \( 4^{1/4} \)
• D. \( 6^{1/6} \)
• E. \( 12^{1/12} \)

Hint:

The function \( f(x) = x^{1/x} \) increases until \( x = e \approx 2.718 \) and then decreases. Since \( 3 \) is the integer closest to \( e \), \( 3^{1/3} \) is the largest among such terms.

Answer 1

The Correct Option is B