Question

Tính:

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

Answer 1

Ta có: \(\left(\sqrt{14}-\sqrt{2}\right)\cdot\sqrt{4+\sqrt{7}}\)

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

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

=7-1=6

Answer 2

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

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

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

\(=\left(\sqrt{7}-1\right)\left(\sqrt{7}+1\right)=7-1=6\)