The product $\sqrt[3]{2}.\sqrt[4]{2}.\sqrt[12]{32}$ equals

1. $\sqrt{2}$

2. 2

3. $\sqrt[12]{2}$

4. $\sqrt[12]{32}$

Given,

$\Rightarrow \sqrt[3]{2}.\sqrt[4]{2}.\sqrt[12]{32} = (2)^{\dfrac{1}{3}}.(2)^{\dfrac{1}{4}}.(2^5)^{\dfrac{1}{12}} \\[1em] = (2)^{\dfrac{1}{3} + \dfrac{1}{4} + \dfrac{5}{12}} \\[1em] = (2)^{\dfrac{4}{12} + \dfrac{3}{12} + \dfrac{5}{12}} \\[1em] = (2)^{\dfrac{12}{12}} \\[1em] = 2^1 = 2.$

Hence, Option 2 is the correct option.