[tex]\sqrt{19-6\sqrt{2} } =\sqrt{1-2*1*3\sqrt{2}+18 } =\sqrt{1-6\sqrt{3} +18} =\sqrt{(1-3\sqrt{2} )^{2} }[/tex]
[tex]\sqrt{(1-3\sqrt{2} )^{2} } = |1-3\sqrt{2} |=-1 +3\sqrt{2}[/tex]
[tex]-1 +3\sqrt{2} + 1 - 3\sqrt{2} = 0[/tex]
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[tex]\sqrt{19-6\sqrt{2} } =\sqrt{1-2*1*3\sqrt{2}+18 } =\sqrt{1-6\sqrt{3} +18} =\sqrt{(1-3\sqrt{2} )^{2} }[/tex]
[tex]\sqrt{(1-3\sqrt{2} )^{2} } = |1-3\sqrt{2} |=-1 +3\sqrt{2}[/tex]
[tex]-1 +3\sqrt{2} + 1 - 3\sqrt{2} = 0[/tex]