[tex] \sqrt{2} \times \sqrt{2 + \sqrt{2}} \times \sqrt{2+\sqrt{2+\sqrt{2}}} \times \sqrt{2-\sqrt{2+\sqrt{2}}} = \\ \\
=\sqrt{2} \times \sqrt{2 + \sqrt{2}} \times \sqrt{\left(2+\sqrt{2+\sqrt{2}}\right) \times \left(2-\sqrt{2+\sqrt{2}}\right)}= \\ \\
=\sqrt{2} \times \sqrt{2 + \sqrt{2}} \times \sqrt{2^2-\left(\sqrt{2+\sqrt{2}}\right)^2}= \\ \\
=\sqrt{2} \times \sqrt{2 + \sqrt{2}} \times \sqrt{4-\left(2+\sqrt{2}\right)}= \\ \\
=\sqrt{2} \times \sqrt{2 + \sqrt{2}} \times \sqrt{4-2-\sqrt{2}}=
[/tex]
[tex]=\sqrt{2} \times \sqrt{2 + \sqrt{2}} \times \sqrt{2-\sqrt{2}}= \\ \\
=\sqrt{2} \times \sqrt{(2 + \sqrt{2}) \times (2-\sqrt{2})}= \\ \\
=\sqrt{2} \times \sqrt{2^2 - (\sqrt{2})^2 }= \\ \\
=\sqrt{2} \times \sqrt{4 - 2 }= \sqrt{2} \times \sqrt{2 }= \boxed{2}[/tex]
