From among $$2^{\frac{1}{2}}, 3^{\frac{1}{3}}, 8^{\frac{1}{8}}$$ and $$9^{\frac{1}{9}}$$, the greatest is

Terms : $$2^{\frac{1}{2}}, 3^{\frac{1}{3}}, 8^{\frac{1}{8}}$$ and $$9^{\frac{1}{9}}$$

L.C.M. (2,3,8,9) = 72

Multiplying the exponents by 72, we get :

= $$2^{\frac{72}{2}}, 3^{\frac{72}{3}}, 8^{\frac{72}{8}}$$ and $$9^{\frac{72}{9}}$$

= $$(2)^{36},(3)^{24},(8)^9,(9)^8$$

Now, clearly, $$(2)^{36}>(8)^9$$ and $$(3)^{24}>(9)^8$$

Now, among $$(2)^{36}$$ and $$(3)^{24}$$

these can be written as : $$(8)^{12}$$ $$<$$ $$(9)^{24}$$

Thus, greatest among these are : $$3^{\frac{1}{3}}$$

=> Ans - (B)