The value of $$\frac{1}{\sqrt{7-4\sqrt{3}}}$$ is closest to

$$ \frac{1}{ \sqrt{7-4\sqrt{3}}}$$

$$\Rightarrow \dfrac {1}{ (2)^2 +  \sqrt {3}^2 - 2\times 2 \sqrt {3}} $$ factor of given expression

$$ \Rightarrow \dfrac{1}{( \sqrt {2- \sqrt{3}})^2}$$ used formula

$$ \Rightarrow \dfrac{1}{(2 - \sqrt {3})} $$(Remove Root )

$$\Rightarrow \dfrac{1}{2 - \sqrt {3}} \times \dfrac{2 +\sqrt {3}}{2 + \sqrt {3}}$$

$$\Rightarrow \dfrac{2 + \sqrt {3}}{4 -3} $$

$$\Rightarrow 2 + \sqrt {3} $$

$$\Rightarrow 2 + 1.73 $$

$$\Rightarrow 3.73 $$

$$\Rightarrow 3.7 $$ Ans