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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?

Mathematics
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  • phi
it does not matter, but generally people write \[ \sqrt{-9} \text{ as }i\sqrt{9} \] so \[ \frac{\cancel{3}}{\cancel{3}i}= \frac{i}{i*i}= -i \]
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?
  • phi
sqrt(-9)*sqrt(-9)= -9

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Ohh...I thought that you would multiply was was inside before simplify the radical...I guess I was wrong. THank you :)
  • phi
I think \[ \sqrt{a \cdot b} =\sqrt{a}\cdot \sqrt{b} \] only works for positive a,b
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.
Yup. THat is the case. Would that also apply to dividing radicals?

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