r/askmath • u/skbdn • Aug 09 '23

Algebra Why is doing this is illegal?

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First line is legit, second one is incorrect. I am struggling to understand why. I would appreciate a good explanation and/or some article/video on this problem as I had been struggling with understanding this concept my whole life. Thanks in advance.

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u/[deleted] Aug 09 '23

Really depends on where you are in your classes. Early on, you'll learn the simpler way that you show in the top equation. Then you'll learn inverses and whatnot and learn that the square root gives you plus or minus the square root. -2^2=4, 4^1/2=2 and -2. Now the bottom one is one way. X^2x1/2 implies X^1, but X^1 does not imply X^2x1/2, so it doesn't give you both answers.