Question

Answer 1

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