Question

How to simplify: 6√v - √4v^2 - √36v + √v^2 ?
I can't find the right answer, but this is what I have written down..

I don't believe the first one can be simplified
-√4v^2 = -√2 * v^2 = -√2 * √v^2 = -2√v^2
-√36v = -√6 * v = -√6 * √v = -6√v
I don't think the last one can be simplified.

So when I combine everything I have:
6√v - 2√v^2 - 6√v + √v^2
6√v - 6√v = 0
- 2√v^2 + √v^2 = -1√v^2

But the only answers that I have to choose from are:
3v
v√v
-v
6v^2

I'm not sure what I've done wrong.

Answer 1

first is the 2nd term
\[ - \sqrt{4v^2} \]
with the v^2 under the radical ?

Answer 2

but in general you should remember that
\[ \sqrt{x^2} = x \]
or
\[ \sqrt{x\cdot x}= x \]

Answer 3

\[6\sqrt{v}- \sqrt{4v^{2}}-\sqrt{36v}+\sqrt{v^{2}}\]
\[6\sqrt{v}- 2v-6\sqrt{v}+v\]

Answer 4

so right away you should be able to simplify the last term

Answer 5

But since the last term is √v^2, wouldn't you just add that with -2√v^2?

Answer 6

yes and thats how u ll arrive at the final answer

Answer 7

Oh okay, so then it would be -v?

Answer 8

Yes!

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