- #1
- 3,802
- 95
This problem had arose in a question I was trying to answer in which I could take two approaches to solve it, but one method would never work, even though I was almost certain there were no algebraic errors made.
Simplified, a section of the problem was as so:
[tex](\sqrt{-a})^3[/tex]
Now, I would go about trying to cube the inside of the root, and cubing a negative gives a negative so I end with:
[tex]\sqrt{-a^3}[/tex]
but after vigorous searching for algebraic errors and finding none, I took another look at this part of the question and (not trusting negatives in roots) went about it like this:
[tex](\sqrt{-a})^3=(i\sqrt{a})^3=i^3\sqrt{a^3}=-i\sqrt{a^3}=-\sqrt{-a^3}[/tex]
which gave me the correct answer. But I'm stumped as to why the first method didn't work
Simplified, a section of the problem was as so:
[tex](\sqrt{-a})^3[/tex]
Now, I would go about trying to cube the inside of the root, and cubing a negative gives a negative so I end with:
[tex]\sqrt{-a^3}[/tex]
but after vigorous searching for algebraic errors and finding none, I took another look at this part of the question and (not trusting negatives in roots) went about it like this:
[tex](\sqrt{-a})^3=(i\sqrt{a})^3=i^3\sqrt{a^3}=-i\sqrt{a^3}=-\sqrt{-a^3}[/tex]
which gave me the correct answer. But I'm stumped as to why the first method didn't work