0\\\\x\sqrt{3}=-\sqrt{3x^2}\; ,\; x<0\\\\3)\; \; \frac{1}{2\sqrt5}=\frac{\sqrt5}{10}\; ,\; \; \frac{1}{\sqrt{a}+5}=\frac{\sqrt{a}-5}{a-25}\\\\4)\; \; (3+\sqrt6)(3-\sqrt6)=9-6=3\\ \\ 5)\; \; \sqrt3\, (2\sqrt3+4\sqrt5)+\sqrt{60}=2\cdot 3+4\sqrt{15}+2\sqrt{15}=6+6\sqrt{15}=6(1+\sqrt{15})" alt="1)\; \; x\sqrt{3x^2}=x\cdot |x|\sqrt3=-x^2\sqrt3\; ,\; \; x<0\\\\\sqrt{24x^2y^2}=2\sqrt6\cdot |x|\cdot |y|=2\sqrt6\cdot xy\; ,\; \; x<0;y<0\\ \\ \sqrt{162}=9\sqrt{2}\\\\2)\; \; 3\sqrt3=\sqrt{9\cdot 3}=\sqrt{27}\\\\x\sqrt{3}=\sqrt{3x^2}\; ,\; x>0\\\\x\sqrt{3}=-\sqrt{3x^2}\; ,\; x<0\\\\3)\; \; \frac{1}{2\sqrt5}=\frac{\sqrt5}{10}\; ,\; \; \frac{1}{\sqrt{a}+5}=\frac{\sqrt{a}-5}{a-25}\\\\4)\; \; (3+\sqrt6)(3-\sqrt6)=9-6=3\\ \\ 5)\; \; \sqrt3\, (2\sqrt3+4\sqrt5)+\sqrt{60}=2\cdot 3+4\sqrt{15}+2\sqrt{15}=6+6\sqrt{15}=6(1+\sqrt{15})" align="absmiddle" class="latex-formula">