Доведіть ,що   ______       _____                          √7 +2√6   -  √7-2√6   число натуральне.

[latex]\sqrt{7+2\sqrt{6}}-\sqrt{7-2\sqrt{6}}=\\\\ \sqrt{6+2\sqrt{6}+1}-\sqrt{6-2\sqrt{6}+1}=\\\\ \sqrt{(\sqrt{6})^2+2*\sqrt{6}*1+1^2}-\sqrt{(\sqrt{6})^2-2*\sqrt{6}*1+1^2}=\\\\ \sqrt{(\sqrt{6}+1)^2}-\sqrt{(\sqrt{6}-1)^2}=\\\\ |\sqrt{6}+1|-|\sqrt{6}-1|=\\\\ \sqrt{6}+1-(\sqrt{6}-1)=\\\\ \sqrt{6}+1-\sqrt{6}+1=2[/latex]