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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?
 one year ago
 one year 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?
 one year ago
 one year ago

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

CalcmathleteBest ResponseYou've already chosen the best response.0
Wait, 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?
 one year ago

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

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

CalcmathleteBest ResponseYou've already chosen the best response.0
Oh 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.
 one year ago

CalcmathleteBest ResponseYou've already chosen the best response.0
Yup. THat is the case. Would that also apply to dividing radicals?
 one year ago
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