How to simplify this?

Question

8 / (square root of -180)

 

Do you rationalize the denominator first? 

Answer 1

8/√-180 =

 

8/i√180 =

 

8/i√180 X (i√180)/(i√180) =

 

 

(8i√180)/ 180i² =

 

 

(8i√180)/-180 =

 

 

(8i√5X36)/-180 =

 

(48i√5)/-180 =

 

(-48i√5)/180 =

 

(-4i√5)/15

Answer 2

 Yes , have to rationalize the denominator.

 

8 / √ -180 = 8 / i √180 = 8 ( -i√180)/(i √180)(-i √180)=

                                                - 8i(√180)/ 180 = -48i√5/ 180=

                                                                              = - 4i√5 /15