Can you please show, in detail ,how this works.Testluv wrote:If x<0, then square root of (x^2) is (-1)*x or -x.
Sqrt(x^2)=x if x>0 or -x if x<0this_time_i_will wrote:Can you please show, in detail ,how this works.Testluv wrote:If x<0, then square root of (x^2) is (-1)*x or -x.
i was working on following lines:
for x<0 ,sq rt(x^2)=>sqrt (-1*x*x)=>x*sqrt(-1)...am stuck here..
Hi!Testluv wrote:When we apply the square root function, the result must be positive. So, we can eliminate negative answers. Choice B is clearly negative.
But because x itself is negative, we can also automatically eliminate choice D (square root can't result in negative).
Similarly, because we can't take the square root of a negative number, we can eliminate choice E.
We don't know x's value, so we can eliminate choice C.
The answer must be choice A!
Because x is negative, "-x" must be positive. The "-" sign doesn't mean we were taking the square root of a negative or that the square root operation yielded a negative result. The "-" doesn't denote the sign of "x". It just tells you to multiply x by -1.
If x<0, then square root of (x^2) is (-1)*x or -x.
|x| = sqrt(x^2) (this is how absolute value is defined)this_time_i_will wrote:Can you please show, in detail ,how this works.Testluv wrote:If x<0, then square root of (x^2) is (-1)*x or -x.
i was working on following lines:
for x<0 ,sq rt(x^2)=>sqrt (-1*x*x)=>x*sqrt(-1)...am stuck here..
thank youTestluv wrote:|x| = sqrt(x^2) (this is how absolute value is defined)this_time_i_will wrote:Can you please show, in detail ,how this works.Testluv wrote:If x<0, then square root of (x^2) is (-1)*x or -x.
i was working on following lines:
for x<0 ,sq rt(x^2)=>sqrt (-1*x*x)=>x*sqrt(-1)...am stuck here..
Both the absolute value and the square root functions must be positive. Therefore:
If x>0, then both sqrt(x^2) and |x| are x;
and
if x<0, then both sqrt(x^2) and |x| are -x.
(if x<0, then because absolute value and square root operations must result in positive, |x| and sqrt(x^2) have to be -x; they can't yield x because x is negative)
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In this question, confusion may arise from wanting/having to diagram "-x" when x itself is negative. (We can't let "-x" be x since "-x" is positive and x is negative).
x is negative. But suppose there is a number, z. If z is positive and equal in absolute value to x, then z = -x or x = -z.
The question asks for sqrt(-x*|x|) or sqrt[(-1)*(x)*|x|]
Subbing "-z" into "x", the question becomes:
what is sqrt[(-1)*(-z)*|-z|]?
Because z is positive, clearly (-1)*(-z) is just z. Likewise |-z| is just z. Thus, we have:
sqrt(z*z)
which is just z
which is equal to -x.
