Question

Please help !

Simplify.

Answer 1

D. -⅓ sqrt(2)

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

D

Explanation:

When we have something like
`\sqrt{(x)/(y) }` , we can write it as:
`(√(x) )/(√(y) )` .

Here, we have:
`\sqrt{(2)/(9) } =(√(2) )/(√(9) ) =(√(2) )/(3)` ,
`\sqrt{(8)/(9) } =(√(8) )/(√(9) ) =(2√(2) )/(3)` , and
`\sqrt{(32)/(9) } =(√(32) )/(√(9) ) =(4√(2) )/(3)` .

Replacing these, we have:

`(√(2) )/(3) -3*(2√(2) )/(3) +(4√(2))/(3) =(√(2) )/(3)-(6√(2) )/(3)+(4√(2))/(3)=(-1)/(3) √(2)`

So, the answer is D.

Hope this helps!