Question

\(\sqrt{3+\sqrt{5}}-\sqrt{4+\sqrt{7}}+\frac{\sqrt{14}}{2}\)

Answer 1

\(\sqrt{3+\sqrt{5}}-\sqrt{4+\sqrt{7}}+\frac{\sqrt{14}}{2}\)

\(\approx1,581\)

Answer 2

=1,5811

Answer 3

Đặt  \(A=\sqrt{3+\sqrt{5}}\)\(-\sqrt{4+\sqrt{7}}\)\(+\frac{\sqrt{14}}{2}\)

\(A\sqrt{2}=\)\(\sqrt{6+2\sqrt{5}}\)\(-\sqrt{8+2\sqrt{7}}\)\(+\sqrt{14}\)

\(A\sqrt{2}=\)\(\sqrt{\left(\sqrt{5}+1\right)^2}\)\(-\sqrt{\left(\sqrt{7}+1\right)^2}\)\(+\sqrt{14}\)

\(A\sqrt{2}=\)\(\sqrt{5}+1-\sqrt{7}-1+\sqrt{14}\)

\(A\sqrt{2}=\)\(\sqrt{5}-\sqrt{7}+\sqrt{14}\)

\(A=\frac{\sqrt{5}}{\sqrt{2}}-\frac{\sqrt{7}}{\sqrt{2}}+\sqrt{7}\)

\(A=\frac{\sqrt{10}-\sqrt{14}}{2}+\sqrt{7}\)