The question:

Quantity A: \sqrt{x^4 + 6x^2 +9}

Quantity B: x^2 +3

My approach:

so I chose D. but it seems the answer is C. So I’ve definitely got some fundamentals wrong. Would love to get some input into what I’m doing wrongly. Thanks!

The question:

Quantity A: \sqrt{x^4 + 6x^2 +9}

Quantity B: x^2 +3

My approach:

\begin{aligned}
\sqrt{x^4 + 6x^2 +9} &= \sqrt{(x^2+3)^2}\\
&= |x^2+3| \text{ because }\sqrt{x^2} = |x| \\
&=x^2+3 \text{ or } -x^2-3
\end{aligned}

so I chose D. but it seems the answer is C. So I’ve definitely got some fundamentals wrong. Would love to get some input into what I’m doing wrongly. Thanks!

Well, the GRE only considers the positive square root. In their official Math Review book, they have had an explanation for it.

Now, you may think that the GRE is being presumptuous in this case, but, in my honest opinion, it’s not really the case.

Because, a square root function is a **radical function**. Notice, the word “function,” we know that a function can’t yield to **two outputs**. A valid function has to have one unique output; otherwise it would violate the core function definition.

To make it clear, I have included the graphs of the both quantities , and yes, their graphs are precisely **the same**. Woot!

Here, the green one is the quantity B which has superimposed on the first quantity A.

Finally, the summary of a radical function in a screenshot.

*Just try to graph a radical function!*

A radical function is cool, at least to me!!

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Wow, thank you so much for the detailed explanation! I always get tripped up with this “radical” situation

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No problem!