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Calcmathlete
 3 years ago
If you have a problem like \[\frac{3}{\sqrt{9}}\]does it matter if you bring the i out first or rationalize first? I believe that it doesn't matter which because it'll come out as i?
Calcmathlete
 3 years ago
If you have a problem like \[\frac{3}{\sqrt{9}}\]does it matter if you bring the i out first or rationalize first? I believe that it doesn't matter which because it'll come out as i?

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phi
 3 years ago
Best ResponseYou've already chosen the best response.1it does not matter, but generally people write \[ \sqrt{9} \text{ as }i\sqrt{9} \] so \[ \frac{\cancel{3}}{\cancel{3}i}= \frac{i}{i*i}= i \]

Calcmathlete
 3 years ago
Best ResponseYou've already chosen the best response.0Wait, if you do it the other way, wouldn't it become i? \[\frac{3}{\sqrt{9}} \times \frac{\sqrt{9}}{\sqrt{9}} \implies \frac{9i}{9} \implies i\]Or did I do something wrong?

Calcmathlete
 3 years ago
Best ResponseYou've already chosen the best response.0Ohh...I thought that you would multiply was was inside before simplify the radical...I guess I was wrong. THank you :)

phi
 3 years ago
Best ResponseYou've already chosen the best response.1I think \[ \sqrt{a \cdot b} =\sqrt{a}\cdot \sqrt{b} \] only works for positive a,b

Calcmathlete
 3 years ago
Best ResponseYou've already chosen the best response.0Oh ok. THat makes sense since you can't really have two answers for something like this. Again, thank you. I'll double check the rule in a second.

Calcmathlete
 3 years ago
Best ResponseYou've already chosen the best response.0Yup. THat is the case. Would that also apply to dividing radicals?
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