The greatest of 2 , 6 3 , 3 4 , 4 5 is = ?

Answer: Option B

LCM of 2, 3, 4, 6 is 12
$$\sqrt{2}=$$  $$2^{\frac{1}{2}}=$$  $$2^{\left(\frac{1}{2}\times \frac{6}{6}\right)}=$$   $$2^{\frac{6}{12}}=$$  $${\left(2^6\right)}^{\frac{1}{12}}=$$  $${\left(64\right)}^{\frac{1}{12}}=$$   $$\text{root}12\text{of}64$$
$$\text{root}6\text{of}3=$$  $$3^{\frac{1}{6}}=$$  $$3^{\left(\frac{1}{6}\times \frac{2}{2}\right)}=$$   $$3^{\frac{2}{12}}=$$  $${\left(3^2\right)}^{\frac{1}{12}}=$$  $${\left(9\right)}^{\frac{1}{12}}=$$   $$\text{root}12\text{of}9$$
$$\text{root}3\text{of}4=$$  $$4^{\frac{1}{3}}=$$  $$4^{\left(\frac{1}{3}\times \frac{4}{4}\right)}=$$  $$4^{\frac{4}{12}}=$$  $${\left(4^4\right)}^{\frac{1}{12}}=$$  $${\left(256\right)}^{\frac{1}{12}}=$$   $$\text{root}12\text{of}256$$
$$\text{root}4\text{of}5=$$  $$5^{\frac{1}{4}}=$$  $$5^{\left(\frac{1}{4}\times \frac{3}{3}\right)}=$$   $$5^{\frac{3}{12}}=$$  $${\left(5^3\right)}^{\frac{1}{12}}=$$  $${\left(125\right)}^{\frac{1}{12}}=$$   $$\text{root}12\text{of}125$$
Clearly $$\text{root}12\text{of}256i.e.,\text{root}3\text{of}4$$     is the greatest.