The value of $$\sqrt{-\sqrt{3}+\sqrt{3+8\sqrt{7+4\sqrt{3}}}}$$ is

$$\sqrt{-\sqrt{3}+\sqrt{3+8\sqrt{7+4\sqrt{3}}}}$$

=$$\sqrt{-\sqrt{3}+\sqrt{3+8\sqrt{7+2\sqrt{12}}}}$$

As per surds calcualation we get

=$$\sqrt{-\sqrt{3}+\sqrt{3+8({\sqrt{4}+\sqrt{3})}}}$$

=$$\sqrt{-\sqrt{3}+\sqrt{3+8({2+\sqrt{3})}}}$$

=$$\sqrt{-\sqrt{3}+\sqrt{3+16+8\sqrt{3}}}$$

=$$\sqrt{-\sqrt{3}+\sqrt{19+8\sqrt{3}}}$$

=$$\sqrt{-\sqrt{3}+\sqrt{19+2\sqrt{48}}}$$

=$$\sqrt{-\sqrt{3}+\sqrt{16}+\sqrt{3}}$$

= $$ \sqrt{16}$$

= 4