I had a homework question, and by the end of my answer I had x squared under a radical. So then I simplified and got just x. My homework marked it wrong and added absolute value signs around it...can someone explain to me why?
#x^2 under a radical?
shrewd oracle
rustic phoenix
I had a homework question, and by the end of my answer I had x squared under a r...
It's wrong because we actually have $$\sqrt{x^2}=|x|$$ To see why it's that, think about what happens when $x=-1$.
odd micaBOT
Kevin S
shrewd oracle
so, you're saying that because we should be dealing with real numbers, not imaginary numbers, that those absolute value lines are there to automatically make everything positive...? you can't have negative numbers, negative dollars...well not in this case, right?
rustic phoenix
so, you're saying that because we should be dealing with real numbers, not imagi...
You didn't mention anything about reality in your question, so I assume it's an algebraic question, and algebraically, what I said is the correct simplification.
proud grotto
so, you're saying that because we should be dealing with real numbers, not imagi...
No, it's because you're squaring x first. Squaring makes it positive.
And when sign isn't indicated outside of a square root sign, you take the positive square root.
rustic phoenix
It seems that your x has a realistic meaning?
shrewd oracle
ah you're right. i just played myself
shrewd oracle
And when sign isn't indicated outside of a square root sign, you take the positi...
i don't really understand this
rustic phoenix
i don't really understand this
it's called the principal value.
shrewd oracle
hold on guys. i might have to dig around to see that homework question properly
proud grotto
i don't really understand this
It is true that 2^2 = 4 and (-2)^2 = 4, but when we write sqrt(4), we only mean for it to be equal to 2.
rustic phoenix
yeah.