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\sqrt{9-5+5-9+5-9+5}

 May 22, 2022
edited by hipie  May 22, 2022
 #1
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+1

\(\sqrt{9-5+5-9+5-9+5} = \sqrt{1} = 1\) by evaluating the expression inside the square root.

 May 22, 2022
 #2
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 May 22, 2022
 #3
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no I think it's 1

hipie  May 23, 2022
edited by hipie  May 24, 2022
 #4
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+1

Because there are absolute value bars inside, which makes it positive. Likewise you don't see a negative sign behind the square root I put. Teachers will remember to test you so have to remember to only use the plus or minus in case of quadratics or something like that. But to put simply square root itself must be positive in the real domain. It doesn't feel right to just say that the sqrt(9) = -3.

hipie  May 23, 2022
edited by hipie  May 23, 2022
 #5
avatar+9461 
+1

hipie: 

In fact, complex square root (in mathematical terms: \(\sqrt{\phantom{a}} : \mathbb C \to \mathbb C\)) is multi-valued, which means it can have multiple outputs for one input. Moreover, for any non-zero complex number, there are always two distinct complex square roots. Therefore, it is actually correct to say that \(\sqrt 9 = \pm 3\). But generally, if it is not specified and the expression inside the square root is real, then we assume that \(\sqrt{\phantom{a}}\) means real-valued square root.

MaxWong  May 23, 2022

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