nisa 2 years ago -√3(√-3) help me pleasee

1. satellite73

$$\sqrt{-3}=\sqrt{3}i$$

2. nisa

i know this is with i agai

3. satellite73

so $-\sqrt{3}\times \sqrt{3}i=-3i$

4. nisa

ohh so anything with a negative is and imaginary number right

5. satellite73

if you have a negative number inside the radical, then it comes outside as $$i$$

6. nisa

yeah because a negative isnt possible in square root

7. satellite73

for example $$\sqrt{-25}=\sqrt{25}i=5i$$ and $\sqrt{-3}=\sqrt{3}i$

8. nisa

i have a few more question like this can i show you and can you tell me if im doing it right?

9. nisa

√-25√-9 its going to be 5i 3i right?

10. satellite73

yes, that would be the first step

11. satellite73

the second step would be to actually multiply and get $5i\times 3i=15i^2=15\times (-1)=-15$

12. nisa

the i goes away?

13. satellite73

yes, because $$i=\sqrt{-1}$$ and so $$i^2=-1$$

14. nisa

oh that makes sense and im sorry i just have two more if u could please check them as well (6i)2 which would be 36i right but if i multiplied 36 by -1 then i get -36 then theres (2+3)(2-3i) im not sure about this one like is it going to be like 5*2-3(-1) ?

15. nisa

thanks for helping me out im stuck with all this and guys are the best :D