SOLUTION: is there more then one way to solve a negative under a radical? if so can you show me the different ways i somewhat understand the consept of the i but i don't know how to bring it

Algebra ->  Radicals -> SOLUTION: is there more then one way to solve a negative under a radical? if so can you show me the different ways i somewhat understand the consept of the i but i don't know how to bring it      Log On


   

Question 399134: is there more then one way to solve a negative under a radical? if so can you show me the different ways i somewhat understand the consept of the i but i don't know how to bring it back into the equation like the square root of -32 i know you can breake it down and bring out the i but what next thnk you for your time sorry if im confusing
EX. (this is where im stuck)
sqrt%28-1%29+%2A+sqrt%28-32%29
%28i%29sqrt%2832%29
then i can break 32 down by:
sqrt%2816%29+%2A+sqrt%282%29
since 16 is the perfect square of 4 you bring 4 out of the radical
4+%2A+sqrt%282%29
i think thats right but i dont know where the i gose or if you can get rid of it entirely??
P.S. i hope that makes sence
if there is another way please show me thanks again
Found 3 solutions by MathLover1, solver91311, richard1234:
Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!

you can do it this way:

sqrt%28-32%29+=sqrt%28-1%2A32%29+

%28i%29sqrt%2832%29
i%28sqrt%2816%29+%2A+sqrt%282%29%29....the i stays here

4i+%2A+sqrt%282%29

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!




Check your work:




John

My calculator said it, I believe it, that settles it
The Out Campaign: Scarlet Letter of Atheism

Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Complex numbers don't really follow the same arithmetic properties when dealing with square roots. For example, sqrt%28-1%29sqrt%28-32%29 does not equal sqrt%28%28-1%29%28-32%29%29 or sqrt%2832%29. Instead, you have to evaluate each radical separately: