SOLUTION: Don't understand what is correct way to do this! Question: What's wrong with using product rule for solving equation -4(under radical sign) times -4 (under the radical sign?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Don't understand what is correct way to do this! Question: What's wrong with using product rule for solving equation -4(under radical sign) times -4 (under the radical sign?       Log On


   

Question 44138: Don't understand what is correct way to do this!
Question: What's wrong with using product rule for solving equation -4(under radical sign) times -4 (under the radical sign?
I would say put both under radical and then square to get correct answer of 4. Notes say what is correct product? Hinted that 4 was not it.

Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28-4%29 is not a real number. So the rule you mentioned is not applicable here.
Such numbers, with -ve sign under the radical, are called imaginery.
sqrt%28-1%29 is called as the imaginery square root of unity and is denoted by i.
So, i=sqrt%28-1%29.
Hence, i%5E2+=+-1.
Now, sqrt%28-4%29 = sqrt%284%2A%28-1%29%29 = sqrt%284%29%2Asqrt%28-1%29 = 2i.
Hence, sqrt%28-4%29%2Asqrt%28-4%29 = 2i%2A2i = 4i%5E2 = -4

To know more about such problems read chapters on imaginery and complex numbers.
All the laws of Mathematical operation which hold for real numbers are not necessarily true with imaginery numbers.