0\; \; \Rightarrow \; \; |a|=+a\; \; ;\; \; \sqrt{a^2}=|a|\; ;\\\\\sqrt{2a^7}=\sqrt{2\cdot a^6\cdot a}=\sqrt{2\cdot (a^3)^2\cdot a}=|a^3|\cdot \sqrt{2a}=|a|^3\cdot \sqrt{2a}=a^3\cdot \sqrt{2a}" alt="a>0\; \; \Rightarrow \; \; |a|=+a\; \; ;\; \; \sqrt{a^2}=|a|\; ;\\\\\sqrt{2a^7}=\sqrt{2\cdot a^6\cdot a}=\sqrt{2\cdot (a^3)^2\cdot a}=|a^3|\cdot \sqrt{2a}=|a|^3\cdot \sqrt{2a}=a^3\cdot \sqrt{2a}" align="absmiddle" class="latex-formula">