## Calcmathlete Group Title 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

1. phi Group Title

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 Group Title

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 Group Title

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

4. Calcmathlete Group Title

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

5. phi Group Title

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

6. Calcmathlete Group Title

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 Group Title

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