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 case
case 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]
