The least one among $${\text{2}}\sqrt 3 {\text{,}}$$  $${\text{2}}\root 4 \of 5 {\text{,}}$$  $$\sqrt 8 {\text{,}}$$  $${\text{3}}\sqrt 2 $$  is = ?

A. $${\text{2}}\sqrt 3 $$

B. $${\text{2}}\root 4 \of 5 $$

C. $$\sqrt 8 $$

D. $${\text{3}}\sqrt 2 $$

Answer: Option C

Solution(By Examveda Team)

$$2\sqrt 3 = {\left( {4 \times 3} \right)^{\frac{1}{2}}} \to {12^{\frac{1}{2}}} \to {12^{\frac{2}{4}}} \to \root 4 \of {144} $$
$$2\root 4 \of 5 = \root 4 \of {\left( {5 \times 16} \right)} \to {80^{\frac{1}{4}}} \to \root 4 \of {80} $$
$$\sqrt 8 = {8^{\frac{1}{2}}} \to {8^{\frac{1}{2}}} \to \boxed{\root 4 \of {64} }\,{\text{smallest}}$$
$$3\sqrt 2 = \sqrt {18} \to {18^{\frac{1}{2}}} \to {18^{\frac{2}{4}}} \to \root 4 \of {324} $$
$$\sqrt 8 \,{\text{ is answer}}$$