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Hi Bunuel, I have a query.... wouldn't \sqrt{x^2}/ x would be equal to +1?
I say so since it's already given in the question that x is a -ve number, so by \sqrt{x^2} we know that we need to consider only the -ve Root.
But in the denominator the variable x would be a -ve number. Hence after the resolution of \sqrt{x^2} one part of the question would be |x|/x, where |x| would give us -x(since the -ve root needs to be considered) and the denominator in isolation is again a -ve number... so the fraction becomes \frac{-x}{-x} = 1.
Hi Bunuel, I have a query.... wouldn't \sqrt{x^2}/ x would be equal to +1?
I say so since it's already given in the question that x is a -ve number, so by \sqrt{x^2} we know that we need to consider only the -ve Root.
But in the denominator the variable x would be a -ve number. Hence after the resolution of \sqrt{x^2} one part of the question would be |x|/x, where |x| would give us -x(since the -ve root needs to be considered) and the denominator in isolation is again a -ve number... so the fraction becomes \frac{-x}{-x} = 1.
Next, the point is that the square root function cannot give negative result (\(\sqrt{some \ expression}\geq{0}\)) and \(\sqrt{x^2}=|x|\), which means that \(\sqrt{x^2}/ x=\frac{|x|}{x}=\frac{-x}{x}=-1\).
Please follow the links in my previous post for more on absolute values.
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There is a step that is off in this question. If you substitute negative y from the get go -(-y) = +y * (-y) leaves you with a negative inside the square root and this cannot happen. Should be written as square root of y*lyl
There is a step that is off in this question. If you substitute negative y from the get go -(-y) = +y * (-y) leaves you with a negative inside the square root and this cannot happen. Should be written as square root of y*lyl
having a hard time understanding this basic rule: \(\sqrt{x^2}=|x|\)
Assuming it's an integer, shouldn't this be the positive integer of x? why |x|
MUST KNOW: \(\sqrt{x^2}=|x|\):
The point here is that since square root function cannot give negative result then \(\sqrt{some \ expression}\geq{0}\).
So \(\sqrt{x^2}\geq{0}\). But what does \(\sqrt{x^2}\) equal to?
Let's consider following examples: If \(x=5\) --> \(\sqrt{x^2}=\sqrt{25}=5=x=positive\); If \(x=-5\) --> \(\sqrt{x^2}=\sqrt{25}=5=-x=positive\).
So we got that: \(\sqrt{x^2}=x\), if \(x\geq{0}\); \(\sqrt{x^2}=-x\), if \(x<0\).
What function does exactly the same thing? The absolute value function: \(|x|=x\), if \(x\geq{0}\) and \(|x|=-x\), if \(x<0\). That is why \(\sqrt{x^2}=|x|\).
For example if x = -5, then \(\sqrt{x^2}=\sqrt{25}=5=|-5|=|x|\)
Having trouble wrapping my head around why \(\sqrt{x^2}\) is equal to |x|
I looked at the post on this page, but did not see any explanation.
For example, how is the equation \(\sqrt{4}\) = {-2, 2} any different from \(\sqrt{2^2}\) = ? Is it because the solution of \(\sqrt{x^2}\) must be equal to the solution of \((\sqrt{x})^2\)? if so, why?
Thanks in advance for any help!
(with regard to bunnel's explanation to xnthic, throughout the explanation bunnel writes "\(\sqrt{25}\) = 5" as though this is given, but my understanding is that \(\sqrt{25}\) could be either positive or negative 5, as either positive or negative 5 squared result in 25. If I am incorrect, then that is most likely the root of my confusion)
Having trouble wrapping my head around why \(\sqrt{x^2}\) is equal to |x|
I looked at the post on this page, but did not see any explanation.
For example, how is the equation \(\sqrt{4}\) = {-2, 2} any different from \(\sqrt{2^2}\) = ? Is it because the solution of \(\sqrt{x^2}\) must be equal to the solution of \((\sqrt{x})^2\)? if so, why?
Thanks in advance for any help!
(with regard to bunnel's explanation to xnthic, throughout the explanation bunnel writes "\(\sqrt{25}\) = 5" as though this is given, but my understanding is that \(\sqrt{25}\) could be either positive or negative 5, as either positive or negative 5 squared result in 25. If I am incorrect, then that is most likely the root of my confusion)
\(\sqrt{4}=2\) ONLY, not 2 or -2. The square root function cannot give negative result. Check here: m26-184464.html#p1729559 _________________
and Square root of Y has to be the positive root.. Thus = y
Thus the answer must be -1-y.
I do understand that \(\sqrt{x^2}\)= |x| ... and if X is -ve then mod x = -x, but we don't have to simplify\(\sqrt{y^2}\) to mod y. We can just take the positive root.. since per GMAT anything under the square root sign is the positive root ?
What am I missing here?
I guess my q is on the GMAT, square root of numbers are ONLY positive..
close
41% (00:47) correct 
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