Verified answer

[tex]\displaystyle\bf\\x^{2} -19x+9=0\\\\\Big(\sqrt{x_{1} } +\sqrt{x_{2} } \Big)^{2} =x_{1} +2\sqrt{x_{1} \cdot x_{2} } +x_{2} =\underbrace{x_{1} +x_{2} }_{19}+2\cdot\sqrt{\underbrace{x_{1} x_{2} }_{9}} =\\\\\\=19+2\sqrt{9} =19+2\cdot 3=19+6=25\\\\\\\sqrt{x_{1} } +\sqrt{x_{2} } =\sqrt{25} =5[/tex]