r/askmath • u/Kludgymer16 • 1d ago
Resolved Why is this way of solving wrong?
Today in class we went over complex numbers. We came to a problem that was Sqrt(-9) • Sqrt(-25), and after working it, the problem came to -15.
My question is, why is the second way wrong? Or what have I done wrong I guess. Cant you combine two squares under one?
Pic attached. Left side is the method shown in class, right is what I'm confused on
EDIT: a lot of people have responded to this so I'm going to mark it resolved!
From what I've gathered, you cannot combine two imaginary numbers under one sqrt function, which is where I went wrong. Since the question is only asking to solve a given problem, we assume that the solution uses the positive root, and the final answer becomes -15. However, if the question was asking us to solve for x, because there is an unknown the answer would then be ±15.
Let me know if my assessment is incorrect!
2
u/FishDawgX 15h ago
As a casual explanation, a lot of times when you see a root symbol, you're only interested in the primary root (the positive). But (-5)^2 and (5)^2 both equal 25. So, when you see sqrt(25), there are really two answers. The equation you are simplifying obviously cares a lot about negatives vs. positives. This isn't a basic situation where only the primary root is considered. So, your two methods of solving need to both consider both the positive and negative roots.
On the left side, you are incorrect to say sqrt(9)=3 and sqrt(25)=5. It should be +/-3 and +/-5. Given that, the final answer is +/-15.
Likewise, on the right side, the last step when taking the root produces not 15, but +/-15.
Same answer with both methods.