Question

\(\sqrt{23-8\sqrt{7}}+\sqrt{8-2\sqrt{7}}\)

Answer 1

\(=\sqrt{23-2.4.\sqrt{7}}+\sqrt{7-2\sqrt{7}.1+1}\\ =\sqrt{16-2.4.\sqrt{7}+7}+\sqrt{\left(\sqrt{7}-1\right)^2}\\ =\sqrt{\left(4-\sqrt{7}\right)^2}+\sqrt{\left(\sqrt{7}-1\right)^2}\\ =\left|4-\sqrt{7}\right|+\left|\sqrt{7}-1\right|\\ =4-\sqrt{7}+\sqrt{7}-1\\ =3\)

Answer 2

\(=4-\sqrt{7}+\sqrt{7}-1=3\)