Question

Answer 1

\(=\left(\sqrt{3}-1\right)\sqrt{2\sqrt{\left(4+\sqrt{3}\right)^2}-4}=\left(\sqrt{3}-1\right)\sqrt{2\left(4+\sqrt{3}\right)-4}\)

\(=\left(\sqrt{3}-1\right)\sqrt{4+2\sqrt{3}}=\left(\sqrt{3}-1\right)\sqrt{\left(\sqrt{3}+1\right)^2}\)

\(=\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)=3-1=2\)

Answer 2

Ta có: \(\left(\sqrt{3}-1\right)\sqrt{2\sqrt{19+8\sqrt{3}}-4}\)

\(=\left(\sqrt{3}-1\right)\sqrt{2\left(4+\sqrt{3}\right)-4}\)

\(=\left(\sqrt{3}-1\right)\sqrt{4+2\sqrt{3}}\)

\(=\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)\)

=2