Question

tinh:

\(\sqrt{6+2\sqrt{8\sqrt{2}-9}}-\sqrt{7-\sqrt{2}}\)

Answer 1

Lời giải:

Ta có:

\(\sqrt{6+2\sqrt{8\sqrt{2}-9}}-\sqrt{7-\sqrt{2}}\)\(=\sqrt{6+2\sqrt{(7-\sqrt{2})(\sqrt{2}-1)}}-\sqrt{7-\sqrt{2}}\)

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

\(=\sqrt{(\sqrt{7-\sqrt{2}}+\sqrt{\sqrt{2}-1})^2}-\sqrt{7-\sqrt{2}}\)

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

Answer 2

Lời giải:

Ta có:

\(\sqrt{6+2\sqrt{8\sqrt{2}-9}}-\sqrt{7-\sqrt{2}}\)\(=\sqrt{6+2\sqrt{(7-\sqrt{2})(\sqrt{2}-1)}}-\sqrt{7-\sqrt{2}}\)

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

\(=\sqrt{(\sqrt{7-\sqrt{2}}+\sqrt{\sqrt{2}-1})^2}-\sqrt{7-\sqrt{2}}\)

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