a.
\(\left(\sqrt{2-\sqrt{3}}-\sqrt{2+\sqrt{3}}\right)^2=2-\sqrt{3}+2+\sqrt{3}-2\sqrt{\left(2-\sqrt{3}\right)\left(2+\sqrt{3}\right)}\)
\(=4-2.\sqrt{4-3}=4-2=2\)
b.
\(\left(1+\sqrt{3}+\sqrt{5}\right)\left(1+\sqrt{3}-\sqrt{5}\right)=\left(1+\sqrt{3}\right)^2-\left(\sqrt{5}\right)^2\)
\(=4+2\sqrt{3}-5=-1+2\sqrt{3}\)
c.
\(\left(3+\sqrt{2}+\sqrt{3}\right)\left(1-\sqrt{2}-\sqrt{3}\right)\)
\(=2\left(1-\sqrt{2}-\sqrt{3}\right)+\left(1+\sqrt{2}+\sqrt{3}\right)\left(1-\sqrt{2}-\sqrt{3}\right)\)
\(=2-2\sqrt{2}-2\sqrt{3}+1-\left(\sqrt{2}+\sqrt{3}\right)^2\)
\(=3-2\sqrt{2}-2\sqrt{3}-\left(5+2\sqrt{6}\right)\)
\(=-2-2\sqrt{2}-2\sqrt{3}-2\sqrt{6}\)
d.
\(\sqrt{6+\sqrt{35}}.\sqrt{6-\sqrt{35}}=\sqrt{\left(6+\sqrt{35}\right)\left(6-\sqrt{35}\right)}=\sqrt{6^2-\sqrt{35}^2}\)
\(=\sqrt{36-35}=1\)
