Please help in simplifying.

Question

shane_b · Answer

Simplify what?

anonymous · Answer

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kinggeorge · Answer

First, square it to get $$3+2\sqrt2$$Now, notice that since 2+1=3 and $2\cdot1=2$, we have that $$3+2\sqrt2=(\sqrt1+\sqrt2)^2=(1+\sqrt2)^2$$Since we square our expression at first, now take the square root to get that $$\sqrt{3+2\sqrt2}=1+\sqrt2$$

anonymous · Answer

So
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would be 1 - root2?

kinggeorge · Answer

I believe so.

kinggeorge · Answer

Actually, it wouldn't. Since $1-\sqrt2<0$, and we can't have that. Therefore, it must be $\sqrt2-1$.

anonymous · Answer

Thanks @KingGeorge . I forgot that a-b)^2 and (b-a)^2 are the same for a moment.

anonymous · Answer

$$3 - 2\sqrt{2} = (1)^2 + (\sqrt{2})^2 - 2(1)(\sqrt{2})$$

So, $$3 - 2\sqrt{2} = (\sqrt{2} - 1)^2$$
Take the square root of this, you will have your answer...

kinggeorge · Answer

Well, I guess it could be $1-\sqrt2$ since square roots can be negative, so technically, it would be better to say that it's $$\pm(1-\sqrt2)$$Likewise, for the first problem, it would be more technically correct to say that it's$$\pm(1+\sqrt2)$$