Answer:
A.) [tex]10\sqrt{5}[/tex]
Step-by-step explanation:
Fist simplify [tex]40\sqrt{40}[/tex] :
[tex]40\sqrt{40}\\\\40\sqrt{4}\sqrt{10}\\\\40*2\sqrt{10}\\\\80\sqrt{10}[/tex]
Now simplify [tex]4\sqrt{8}[/tex] :
[tex]4\sqrt{8}\\\\4\sqrt{4}\sqrt{2} \\\\4*2\sqrt{2}\\\\8\sqrt{2}[/tex]
Insert both into expression:
[tex]\frac{80\sqrt{10}}{8\sqrt{2}}[/tex]
Simplify:
[tex]\frac{10\sqrt{10}}{\sqrt{2}}[/tex]
Rationalize:
[tex]\frac{\sqrt{2}}{\sqrt{2}}*\frac{10\sqrt{10}}{\sqrt{2}}\\\\\frac{10\sqrt{20}}{\sqrt{4}}\\\\\frac{10\sqrt{20} }{2}[/tex]
Simplify:
[tex]5\sqrt{20}[/tex]
Convert to simplest radical form:
[tex]5\sqrt{4*5} \\\\5\sqrt{4}\sqrt{5}\\\\5*2\sqrt{5}\\\\10\sqrt{5}[/tex]
:Done
