[tex]\text{Put the value of x to the expression}\\\\\sqrt{x+3};\ x=15\\\\\sqrt{15+3}=\sqrt{18}=\sqrt{9\cdot2}=\sqrt9\cdot\sqrt2=\boxed{3\sqrt2}[/tex]
[tex]\text{Put the value of x to the expression}\\\\\dfrac{6}{\sqrt{x}},\ x=3\\\\\dfrac{6}{\sqrt3}=\dfrac{6\cdot\sqrt3}{\sqrt3\cdot\sqrt3}=\dfrac{6\sqrt3}{3}=\boxed{2\sqrt3}[/tex]
[tex]\text{Put the value of x to the expression}\\\\4\sqrt{x+1}-3\sqrt{2x+6},\ x=3\\\\4\sqrt{3+1}-3\sqrt{2(3)+6}=4\sqrt4-3\sqrt{6+6}=4(2)-3\sqrt{12}\\\\=8-3\sqrt{4\cdot3}=8-3\sqrt4\cdot\sqrt3=8-3(2)\cdot\sqrt3=\boxed{8-6\sqrt3}[/tex]
