Arranging the following in descending order, we get
$$\sqrt[3]{4},\sqrt{2},\sqrt[6]{3},\sqrt[4]{5}$$

Expression : $$\sqrt[3]{4},\sqrt{2},\sqrt[6]{3},\sqrt[4]{5}$$

= $$4^{\frac{1}{3}} , 2^{\frac{1}{2}} , 3^{\frac{1}{6}} , 5^{\frac{1}{4}}$$

Now, L.C.M. of the powers i.e. 3,2,4,6 = 12

Multiplying the powers by 12 in each of the numbers, we get :

= $$4^4 , 2^6 , 3^2 , 5^3$$

= $$256 , 64 , 9 , 125$$

Now arranging them in descending order,

=> $$256 > 125 > 64 > 9$$

$$\equiv$$ $$\sqrt[3]{4} > \sqrt[4]{5} > \sqrt{2} > \sqrt[6]{3}$$