Question

ДАЮ 100 БАЛЛОВ !!!
пожалуйста

Answer 1

$\displaystyle\bf\\1)\\\\2a\sqrt{3} =\sqrt{(2a)^{2}\cdot 3 } =\sqrt{4a^{2}\cdot 3 }=\sqrt{12a^{2} } \\\\2)\\\\b\sqrt{\frac{1}{b} }= \sqrt{\frac{|b|^{2} }{b} } \\\\3)\\\\3x^{2} \sqrt{x} =\sqrt{(3x^{2} )^{2}\cdot x } =\sqrt{9x^{4}\cdot x } =\sqrt{9x^{5} } \\\\4)\\\\3\sqrt{3} =\sqrt{3^{2}\cdot 3 } =\sqrt{9\cdot 3}=\sqrt{27} \\\\27 > 12 \ \ \ \Rightarrow \ \ \ \sqrt{27} > \sqrt{12} \ \ \ \Rightarrow \ \ \ \boxed{ 3\sqrt{3} > \sqrt{12} }$

$\displaystyle\bf\\5)\\\\3\sqrt{5} =\sqrt{3^{2}\cdot 5 } =\sqrt{9\cdot 5}=\sqrt{45} \\\\20 < 45 \ \ \ \Rightarrow \ \ \ \sqrt{20} < \sqrt{45} \ \ \ \Rightarrow \ \ \ \boxed{ \sqrt{20} < 3\sqrt{5} }\\\\6)\\\\5\sqrt{4} =\sqrt{5^{2}\cdot 4 } =\sqrt{25\cdot 4}=\sqrt{100}\\\\4\sqrt{5} =\sqrt{4^{2}\cdot 5 } =\sqrt{16\cdot 5}=\sqrt{80}\\\\100 > 80 \ \ \ \Rightarrow \ \ \ \sqrt{100} > \sqrt{80} \ \ \Rightarrow \ \ \boxed{5\sqrt{4} > 4\sqrt{5} }$

$\displaystyle\bf\\7)\\\\2\sqrt{5} =\sqrt{2^{2}\cdot 5 } =\sqrt{4\cdot 5}=\sqrt{20}\\\\3\sqrt{2} =\sqrt{3^{2}\cdot 2 } =\sqrt{9\cdot 2}=\sqrt{18}\\\\20 > 18 \ \ \ \Rightarrow \ \ \ \sqrt{20} > \sqrt{18} \ \ \Rightarrow \ \ \boxed{2\sqrt{5} > 3\sqrt{2} }$