Is √x²=x an indentity (true for all values of x)?

Question

Answer:


Explain your answer:

Answer 1

I belive that the sqrt of x^2 is = to the absolute value of x..

since x could be positve or negative..

here, x can only be a postive, value since the root of any value cannot be negative, if x is a negative value, it would not be true..

Answer 2

Not true for all values of x. Like others said,
√x²=|x|
Not just x.
x can be both positive or negative. Negative numbers squared are positive. Only positive numbers can be square rooted (not sure that's a word) or else they become imaginary. And the square root of any positive number can also be negative. Like -1 times -1, equals 1.

Answer 3

True. As x is squared (^2) it will always be a positive number, or 0.
But the right answer is: Sq Rt x^2 = +x & -x

Answer 4

No. Consider x = -2, for which it is false. Square roots are always taken to be positive.

Answer 5

It is false because if x=-4 ( any negative ) x^2=16
and sqrt(x^2)=4
In general sqrt(x^2) = I x I

Answer 6

√(x²)=|x|.
(√x)²=x or is undefined over the reals.