# Thread: √Combine Like Terms?

1. ## √Combine Like Terms?

This is my first post, thank you for your consideration.

My question regards the process of adding radicals.

If it follows that
√8 = √2+4 = 2√2.

When why doesn't 2√2 + 2√2 = 2+2+√2+√2; instead of the correct answer of 4√2. How come the other like terms are discarted?

I know there is a super simple answer to this which will make me look like a complete mule, but I would rather be an informed mule than a proud fool.

2. ## Re: √Combine Like Terms?

What you want is:

$\displaystyle \sqrt{8}=\sqrt{4\cdot2}=\sqrt{4}\cdot\sqrt{2}=2 \sqrt{2}$

and:

$\displaystyle 2\sqrt{2}+2\sqrt{2}=2\sqrt{2}(1+1)=2(2\sqrt{2})=4 \sqrt{2}$

3. ## Re: √Combine Like Terms?

Hello, Enthusiast!

Welcome aboard!

Why doesn't 2√2 + 2√2 = 2 + 2 + √2 + √2 ?

It should be obvious that we don't add like that.

$\displaystyle 2\sqrt{2}$ is simply "two times a thing".

Let $\displaystyle x$ = thing.

Then you have: .$\displaystyle 2x + 2x$

Got it?

4. ## Re: √Combine Like Terms?

I think I got really focused upon the deconstruction of the radicand and some how my "brain head" as Trippy would say got addition and multipication mixed up....I don't know. Thanks for the clarification everyone.