Question

\(\sqrt{7-2\sqrt{6}}+\sqrt{7+2\sqrt{6}}\)

Answer 1

\(\sqrt{7-2\sqrt{6}}+\sqrt{7+2\sqrt{6}}=\sqrt{\left(\sqrt{6}-1\right)^2}+\sqrt{\left(\sqrt{6}+1\right)^2}=\left|\sqrt{6}-1\right|+\left|\sqrt{6}+1\right|=\sqrt{6}-1+\sqrt{6}+1=2\sqrt{6}\)

Answer 2

\(\sqrt{7-2\sqrt{6}}+\sqrt{7+2\sqrt{6}}\)

\(=\sqrt{6}-1+\sqrt{6}+1\)

\(=2\sqrt{6}\)