Answer:
b. [tex]-25\sqrt{2}[/tex]
Step-by-step explanation:
Given:
The expression to simplify is given as:
[tex]-3\sqrt{162}+2\sqrt{200}-9\sqrt{8}[/tex]
Let us simplify each term and then add them together.
[tex]-3\sqrt{162}=-3\sqrt{81\times2}=-3\times 9\sqrt{2}=-27\sqrt{2}[/tex]
[tex]2\sqrt{200}=2\sqrt{100\times 2}=2\times 10\sqrt{2}=20\sqrt{2}[/tex]
[tex]-9\sqrt{8}=-9\sqrt{4\times2}=-9\times 2\sqrt{2}=-18\sqrt{2}[/tex]
Now, add all the results obtained above. This gives,
[tex]-27\sqrt{2}+20\sqrt{2}-18\sqrt{2}[/tex]
Taking [tex]\sqrt2[/tex] out as it is a common factor, we get
[tex]=\sqrt{2}(-27+20-18)\\=\sqrt2(-25)\\=-25\sqrt{2}[/tex]
Therefore, the correct option is b.
