\(\sqrt{8-2\sqrt{7}}+\sqrt{23-8\sqrt{7}}\)
=\(\sqrt{\sqrt{7}^2-2.\sqrt{7}.1+1^2}+\sqrt{4^2-2.4.\sqrt{7}+\sqrt{7}^2}\)
=\(\sqrt{\left(\sqrt{7}-1\right)^2}+\sqrt{\left(4-\sqrt{7}\right)^2}\)
=\(\left|\sqrt{7}-1\right|+\left|4-\sqrt{7}\right|\)
=\(\sqrt{7}-1+4-\sqrt{7}\)
=3
\(\sqrt{8-2\sqrt{7}}\) + \(\sqrt{23-8\sqrt{7}}\)
= \(\sqrt{7-2\sqrt{7}+1}\) + \(\sqrt{16-8\sqrt{7}+7}\)
= \(\sqrt{\left(\sqrt{7}\right)^2-2\sqrt{7}+1^2}\) + \(\sqrt{4^2-2.4.\sqrt{7}+\left(\sqrt{7}\right)^2}\)
= \(\sqrt{\left(\sqrt{7}-1\right)^2}\) + \(\sqrt{\left(4-\sqrt{7}\right)^2}\)
= \(\left|\sqrt{7}-1\right|\) + \(\left|4-\sqrt{7}\right|\)
= \(-\)( \(\sqrt{7}-1\)) + ( \(4-\sqrt{7}\)) ( vì \(\sqrt{7}-1\)< 0; \(4-\sqrt{7}\)>0)
= \(-1+\sqrt{7}\) + \(4-\sqrt{7}\)
= 3
