a) Sửa đề: \(A=\sqrt{8+2\sqrt{7}}-\sqrt{7}\)
Ta có: \(A=\sqrt{8+2\sqrt{7}}-\sqrt{7}\)
\(=\sqrt{7+2\cdot\sqrt{7}\cdot1+1}-\sqrt{7}\)
\(=\sqrt{\left(\sqrt{7}+1\right)^2}-\sqrt{7}\)
\(=\left|\sqrt{7}+1\right|-\sqrt{7}\)
\(=\sqrt{7}+1-\sqrt{7}\)
=1
b) Ta có: \(B=\sqrt{7+4\sqrt{3}}-2\sqrt{3}\)
\(=\sqrt{4+2\cdot2\cdot\sqrt{3}+3}-2\sqrt{3}\)
\(=\sqrt{\left(2+\sqrt{3}\right)^2}-2\sqrt{3}\)
\(=\left|2+\sqrt{3}\right|-2\sqrt{3}\)
\(=2+\sqrt{3}-2\sqrt{3}\)
\(=2-\sqrt{3}\)
c) Ta có: \(C=\sqrt{14-2\sqrt{13}}+\sqrt{14+2\sqrt{13}}\)
\(=\sqrt{13-2\cdot\sqrt{13}\cdot1+1}+\sqrt{13+2\cdot\sqrt{13}\cdot1+1}\)
\(=\sqrt{\left(\sqrt{13}-1\right)^2}+\sqrt{\left(\sqrt{13}+1\right)^2}\)
\(=\left|\sqrt{13}-1\right|+\left|\sqrt{13}+1\right|\)
\(=\sqrt{13}-1+\sqrt{13}+1\)
\(=2\sqrt{13}\)
d) Ta có: \(D=\sqrt{22-2\sqrt{21}}-\sqrt{22+2\sqrt{21}}\)
\(=\sqrt{21-2\cdot\sqrt{21}\cdot1+1}-\sqrt{21+2\cdot\sqrt{21}\cdot1+1}\)
\(=\sqrt{\left(\sqrt{21}-1\right)^2}-\sqrt{\left(\sqrt{21}+1\right)^2}\)
\(=\left|\sqrt{21}-1\right|-\left|\sqrt{21}+1\right|\)
\(=\sqrt{21}-1-\left(\sqrt{21}+1\right)\)
\(=\sqrt{21}-1-\sqrt{21}-1\)
=-2
