Question

Thực hiện phép tính:

\(\left(\sqrt{14}+\sqrt{6}\right)\).\(\left(\sqrt{5-\sqrt{21}}\right)\)

Answer 1

\(\left(\sqrt{14}+\sqrt{6}\right)\left(\sqrt{5-\sqrt{21}}\right)\)

\(=\left(\sqrt{7}+\sqrt{3}\right)\left(\sqrt{10-2\sqrt{21}}\right)\)

\(=\left(\sqrt{7}+\sqrt{3}\right)\left(\sqrt{7}-\sqrt{3}\right)\)

\(=4\)

Answer 2

\(\left(\sqrt{14}+\sqrt{6}\right)\left(\sqrt{5-\sqrt{21}}\right)\)

\(=\sqrt{2}\left(\sqrt{7}+\sqrt{3}\right)\left(\sqrt{5-\sqrt{21}}\right)\)

\(=\left(\sqrt{7}+\sqrt{3}\right)\left[\sqrt{10-2\sqrt{21}}\right]\)

\(=\left(\sqrt{7}+\sqrt{3}\right)\sqrt{\left(\sqrt{7}-\sqrt{3}\right)^2}\)

\(=\left(\sqrt{7}+\sqrt{3}\right)\left(\sqrt{7}-\sqrt{3}\right)\)

\(=7-3=4\)