Answer:
D
Step-by-step explanation:
When we have something like [tex]\sqrt{\frac{x}{y} }[/tex] , we can write it as: [tex]\frac{\sqrt{x} }{\sqrt{y} }[/tex] .
Here, we have: [tex]\sqrt{\frac{2}{9} } =\frac{\sqrt{2} }{\sqrt{9} } =\frac{\sqrt{2} }{3}[/tex] , [tex]\sqrt{\frac{8}{9} } =\frac{\sqrt{8} }{\sqrt{9} } =\frac{2\sqrt{2} }{3}[/tex] , and [tex]\sqrt{\frac{32}{9} } =\frac{\sqrt{32} }{\sqrt{9} } =\frac{4\sqrt{2} }{3}[/tex] .
Replacing these, we have:
[tex]\frac{\sqrt{2} }{3} -3*\frac{2\sqrt{2} }{3} +\frac{4\sqrt{2}}{3} =\frac{\sqrt{2} }{3}-\frac{6\sqrt{2} }{3}+\frac{4\sqrt{2}}{3}=\frac{-1}{3} \sqrt{2}[/tex]
So, the answer is D.
Hope this helps!
