[tex]a)\ \ 2\sqrt{3}=\sqrt{2^2\cdot3}=\sqrt{4\cdot3}=\sqrt{12}\\\\b)\ \ 3\sqrt{5}=\sqrt{3^2\cdot5}=\sqrt{9\cdot5}=\sqrt{45}\\\\c)\ \ 2\sqrt[3]{4}=\sqrt[3]{2^3\cdot4}=\sqrt[3]{8\cdot4}=\sqrt[3]{32}\\\\d)\ \ a\sqrt{2}=\sqrt{a^2\cdot2}=\sqrt{2a^2}[/tex]
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[tex]a)\ \ 2\sqrt{3}=\sqrt{2^2\cdot3}=\sqrt{4\cdot3}=\sqrt{12}\\\\b)\ \ 3\sqrt{5}=\sqrt{3^2\cdot5}=\sqrt{9\cdot5}=\sqrt{45}\\\\c)\ \ 2\sqrt[3]{4}=\sqrt[3]{2^3\cdot4}=\sqrt[3]{8\cdot4}=\sqrt[3]{32}\\\\d)\ \ a\sqrt{2}=\sqrt{a^2\cdot2}=\sqrt{2a^2}[/tex]