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