Discussion

Explanation:

Given, 3^1/2, 4^1/5, 5^1/4

LCM (2, 5, 4) = 20

Raising all the numbers to power 20, we get:

⇒ ${\left(3^{\frac{1}{2}}\right)}^{20}, {\left(4^{\frac{1}{5}}\right)}^{20}, {\left(5^{\frac{1}{4}}\right)}^{20}$

⇒ 3¹⁰, 4⁴, 5⁵

⇒ 9⁵, 256, 3125

⇒ 81 × 729, 256, 3125

Since, 81 × 729 > 3125 > 256

⇒ 3^1/2 > 5^1/4 > 4^1/5

Hence, option (d).

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