MHB How can we simplify this expression involving square roots?

[Zoey323]

$$4\sqrt{n^{2}}+\sqrt{m^{2}n-\sqrt{4n^{2}}}-\sqrt{mn^{2}}$$
I don't even know where to start, I know the teacher said to distribute but distibute what?

 

[topsquark]

$$4\sqrt{n^{2}}+\sqrt{m^{2}n-\sqrt{4n^{2}}}-\sqrt{mn^{2}}$$
I don't even know where to start, I know the teacher said to distribute but distibute what?

Well, you could start by simplifying [math]\sqrt{n^2}[/math]. What is that?

-Dan

 

[Amad27]

$$4\sqrt{n^{2}}+\sqrt{m^{2}n-\sqrt{4n^{2}}}-\sqrt{mn^{2}}$$
I don't even know where to start, I know the teacher said to distribute but distibute what?

Not necessarily distribute but observe and simplify.

Use facts like

$\sqrt(n^2) = n$ and facts like $\sqrt(4) = 2$

To start you off, notice,

$4\sqrt(n^2) = 4n$

Also remember facts like

$\sqrt(ab) = \sqrt(a)\cdot\sqrt(b)$

 

[MarkFL]

If $n$ is known to be non-negative, then we can write:

$$\sqrt{n^2}=n$$

Otherwise, we should write by definition:

$$\sqrt{n^2}=|n|$$