Question

Please help ! Simplify.

Answer 1

Answer:

D. -⅓ sqrt(2)

Step-by-step explanation:

8 = 2²×2

32 = 4²×2

sqrt(2/9) - 3sqrt(2²×2/9) + sqrt(4²×2/9)

sqrt(2/9) - 6sqrt(2/9) + 4sqrt(2/9)

sqrt(2/9) [1 - 6 + 4]

sqrt(2/9)(-1)

9 = 3²

-sqrt(2/3²)

-⅓sqrt(2)

Answer 2

Answer:

D

Step-by-step explanation:

When we have something like $\sqrt{\frac{x}{y} }$ , we can write it as: $\frac{\sqrt{x} }{\sqrt{y} }$ .

Here, we have: $\sqrt{\frac{2}{9} } =\frac{\sqrt{2} }{\sqrt{9} } =\frac{\sqrt{2} }{3}$ ,  $\sqrt{\frac{8}{9} } =\frac{\sqrt{8} }{\sqrt{9} } =\frac{2\sqrt{2} }{3}$ , and $\sqrt{\frac{32}{9} } =\frac{\sqrt{32} }{\sqrt{9} } =\frac{4\sqrt{2} }{3}$ .

Replacing these, we have:

$\frac{\sqrt{2} }{3} -3*\frac{2\sqrt{2} }{3} +\frac{4\sqrt{2}}{3} =\frac{\sqrt{2} }{3}-\frac{6\sqrt{2} }{3}+\frac{4\sqrt{2}}{3}=\frac{-1}{3} \sqrt{2}$

So, the answer is D.

Hope this helps!