Question

Add or subtract terms whenever possible

-3√162 + 2√200 - 9√8


a. -187√2


b. -25√2


c. -3√2


d. 187√2

Answer 1

b.
`-25√(2)`

Explanation:

Given:

The expression to simplify is given as:

`-3√(162)+2√(200)-9√(8)`

Let us simplify each term and then add them together.

`-3√(162)=-3√(81*2)=-3* 9√(2)=-27√(2)`

`2√(200)=2√(100* 2)=2* 10√(2)=20√(2)`

`-9√(8)=-9√(4*2)=-9* 2√(2)=-18√(2)`

Now, add all the results obtained above. This gives,

`-27√(2)+20√(2)-18√(2)`

Taking
`\sqrt2` out as it is a common factor, we get

`=√(2)(-27+20-18)\\=\sqrt2(-25)\\=-25√(2)`

Therefore, the correct option is b.