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I've started my pre-calculus course on Khan Academy and I came across the "principal" square root, where the radical sign is used. It's said that only the positive square root of the nth number will be rooted.

Now my question is, is there an "opposite" square root? As in the negative square root, or even both?

For example: $\sqrt{16} = 4$, but not $-4$.

What kind of symbol, or "function" would result in $-4$? Or even $4$ and/or $-4$?

Xander Henderson
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sjpwhite
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    The short answer is: the function $-\sqrt{x}$. For longer answers, there are zillions of posts on this site about square root functions; try searching. Start with this one which I found in the "related" list to the right of your question. – Lee Mosher Apr 22 '25 at 13:45

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$\sqrt{16}=+4 $ by definition. If you solve the equation $x^2=16$ you get two results, $x=+4$ and $x=-4$. If you want $\sqrt{16}$ negative you just write $-\sqrt{16}$.

Xander Henderson
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trula
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