Q:

Which choices are equivalent to the expression below? Check all that apply. 6√3A. √18 * √6 B. √108C. √3 * √6D. √54E. √3 * √36 F. 108

Accepted Solution

A:
Answer:case A. [tex]\sqrt{18}*\sqrt{6}[/tex]case B. [tex]\sqrt{108}[/tex]case E. [tex]\sqrt{3}*\sqrt{36}[/tex]Step-by-step explanation:we have[tex]6\sqrt{3}[/tex]we know that[tex]6\sqrt{3}=\sqrt{36*3}=\sqrt{108}[/tex]Verify each casecase A) [tex]\sqrt{18}*\sqrt{6}[/tex][tex]\sqrt{18}*\sqrt{6}=\sqrt{18*6}=\sqrt{108}[/tex]therefore[tex]\sqrt{18}*\sqrt{6}[/tex] is equivalent to [tex]6\sqrt{3}[/tex]case B) [tex]\sqrt{108}[/tex]so[tex]\sqrt{108}[/tex] is equivalent to [tex]6\sqrt{3}[/tex]case C) [tex]\sqrt{3}*\sqrt{6}[/tex][tex]\sqrt{3}*\sqrt{6}=\sqrt{18}[/tex]therefore[tex]\sqrt{18}[/tex] is not equivalent to [tex]6\sqrt{3}[/tex]case D) [tex]\sqrt{54}[/tex]so[tex]\sqrt{54}[/tex] is not equivalent to [tex]6\sqrt{3}[/tex]case E) [tex]\sqrt{3}*\sqrt{36}[/tex][tex]\sqrt{3}*\sqrt{36}=\sqrt{108}[/tex]therefore[tex]\sqrt{3}*\sqrt{36}[/tex] is equivalent to [tex]6\sqrt{3}[/tex]case F) [tex]108[/tex]so[tex]108[/tex] is not equivalent to [tex]6\sqrt{3}[/tex]