## 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?

1. phi

it does not matter, but generally people write $\sqrt{-9} \text{ as }i\sqrt{9}$ so $\frac{\cancel{3}}{\cancel{3}i}= \frac{i}{i*i}= -i$

2. Calcmathlete

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?

3. phi

sqrt(-9)*sqrt(-9)= -9

4. Calcmathlete

Ohh...I thought that you would multiply was was inside before simplify the radical...I guess I was wrong. THank you :)

5. phi

I think $\sqrt{a \cdot b} =\sqrt{a}\cdot \sqrt{b}$ only works for positive a,b

6. Calcmathlete

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.

7. Calcmathlete

Yup. THat is the case. Would that also apply to dividing radicals?