Question

\(\left(4-\sqrt{7}\right)\left(\sqrt{14}+\sqrt{2}\right)\sqrt{4+\sqrt{7}}\)

Answer 1

\(\left(4-\sqrt{7}\right)\left(\sqrt{14}+\sqrt{2}\right)\left(\sqrt{4+\sqrt{7}}\right)\)

\(=\left(4-\sqrt{7}\right)\left(\sqrt{7}+1\right)\left(\sqrt{8+2\sqrt{7}}\right)\)

\(=\left(4-\sqrt{7}\right)\left(\sqrt{7}+1\right)\left(\sqrt{\left(\sqrt{7}+1\right)^2}\right)\)

\(=\left(4-\sqrt{7}\right)\left(\sqrt{7}+1\right)^2\)

\(=\left(4-\sqrt{7}\right)\left(8+2\sqrt{7}\right)\)

\(=2\left(4-\sqrt{7}\right)\left(4+\sqrt{7}\right)\)

\(=2\left(16-7\right)=2.9=18\)

Vậy : \(\left(4-\sqrt{7}\right)\left(\sqrt{14}+\sqrt{2}\right)\left(\sqrt{4+\sqrt{7}}\right)=18\)