Which among the following is the largest?
21/2, 31/3, 41/4 and 61/6

To determine which of the numbers \( \frac{2^{1/2}}, \frac{3^{1/3}}, \frac{4^{1/4}}, \frac{6^{1/6}} \) is the largest, we can compare their values by calculating them individually:

1. \( 2^{1/2} = \sqrt{2} \approx 1.414 \)
2. \( 3^{1/3} \approx 1.442 \)
3. \( 4^{1/4} = \sqrt[4]{4} \approx 1.414 \)
4. \( 6^{1/6} \approx 1.348 \)

Among these values:

- \( 2^{1/2} \approx 1.414 \)
- \( 3^{1/3} \approx 1.442 \)
- \( 

Which among the following is the largest? 21/2, 31/3, 41/4 and 61/6

Explore and compare the values of fractions 21/2, 31/3, 41/4, and 61/6 to determine which is the largest. This problem involves understanding fraction comparison and approximation. Suitable for Grades 7-9.

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