Ta đặt: \(A=\sqrt{\sqrt{7}-\sqrt{3}}-\sqrt{\sqrt{7}+\sqrt{3}}\)

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

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

<=> \(A^2=2\sqrt{7}-2\sqrt{7-3}\)

<=> \(A^2=2\sqrt{7}-2\sqrt{4}=2\left(\sqrt{7}-2\right)\)

=> \(A=\sqrt{2\left(\sqrt{7}-2\right)}\)

Thay vào ta được:

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

a. \(=\sqrt{2}.\left(\sqrt{7}+\sqrt{8}\right)\sqrt{5-\sqrt{3}\sqrt{7}}\)

\(=\left(\sqrt{7}+\sqrt{8}\right)\sqrt{3-2\sqrt{3}.\sqrt{7}+7}\)

\(=\left(\sqrt{7}+\sqrt{8}\right)\sqrt{\left(\sqrt{7}-\sqrt{3}\right)^2}\)

\(=\left(\sqrt{7}+\sqrt{8}\right)\left(\sqrt{7}-\sqrt{3}\right)\)

Rồi nhân ra. bạn làm tiếp nhé. Tuy nhiên minh nghĩ bạn bị nhầm đề. là \(\sqrt{6}\) chứ không phải căn 16

b. \(=\frac{5\left(\sqrt{21}+1\right)}{21-16}+\frac{\sqrt{3}.\sqrt{7}\left(\sqrt{3}-\sqrt{7}\right)}{-\left(\sqrt{3}-\sqrt{7}\right)}\)

\(=\sqrt{21}+4-\sqrt{21}=4\)

Mình coi lại r  \(\sqrt{16}\) nhé

Tu bieu thuc \(\Leftrightarrow\frac{3.\left(\sqrt{7}+2\right)}{\left(\sqrt{7}-2\right)\left(\sqrt{7}+2\right)}-\frac{14\sqrt{7}}{7}+|\sqrt{7}-2|\)

                    \(\Leftrightarrow3\sqrt{7}+6-2\sqrt{7}+\sqrt{7}-2=2\sqrt{7}+4\)

a) \(=\frac{7-4\sqrt{3}+7+4\sqrt{3}}{\left(7+4\sqrt{3}\right)\left(7-4\sqrt{3}\right)}=\frac{14}{49-48}=14\)

b) \(=\frac{15\left(\sqrt{6}-1\right)}{\left(\sqrt{6}+1\right)\left(\sqrt{6}-1\right)}-\frac{5\sqrt{6}}{5}+\frac{4\sqrt{3}-12\sqrt{2}}{\sqrt{6}\left(\sqrt{3}-\sqrt{2}\right)}\)