Question

\(\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}\)

Answer 1

\(=\sqrt{4+\sqrt{15}}.\left(\sqrt{4+\sqrt{15}}.\sqrt{4-\sqrt{15}}\right).\left(\sqrt{10}-\sqrt{6}\right)\)

=\(\sqrt{4+\sqrt{15}}.\left(\sqrt{10}-\sqrt{6}\right)=\sqrt{2}.\sqrt{4+\sqrt{15}}.\left(\sqrt{5}-\sqrt{3}\right)\)

=\(\sqrt{3+2\sqrt{3.5}+5}.\left(\sqrt{5}-\sqrt{3}\right)\)

=\(\sqrt{\left(\sqrt{5}+\sqrt{3}\right)^2}.\left(\sqrt{5}-\sqrt{3}\right)\)

=\(\left(\sqrt{5}-\sqrt{3}\right)\left(\sqrt{5}+\sqrt{3}\right)=5-3=2\)