What is the sqrt of x^2?

Question

Teacher said it was absolute value x. Why?

Answer 1

By definition, the square root of x^2 is the positive number we need to square in order to obtain x^2. The two numbers we need to square in order to get x^2 are x and -x, so if x>0 then x is the positive one and if x<0 then -x is the positive one, thus the correct answer is the absolute value of x, which is, by definition, x if x>=0 and -x if x<0.

E.g., (-5)^2=25 and the two possible square roots are -5 and +5, but only 5 is the positive one, and abs(-5)=5.

(PS.: Some people say that there are two square roots, a positive and a negative one, but in a strict sense, the square root sign denotes a function, which can only have one value, and the positive one is used by convention. In our case, the positive one is the absolute value of x.)

Answer 2

i was just about to say the same thing before i read what you had under "What is"

here is what most people would say sqrt(x^2), the sqrt and ^2 cancel out leaving you with "x" as the answer, which is only partly right.

lets say "x" < 0, this would give you sqrt((-1)^2) = -1, which is incorrect, since sqrt((-1)^2 = sqrt(1) = 1 and not -1, so you would have to have a positive "x" value for that to work, so the answer would be

|x| and not x

Answer 3

it will be +/- x
if the negative sign is not admissible in those cases it will be the absolute value
for example let the area of a square be=x^2= 400 m^2
now the side of the square will be rt x^2 or rt 400
we cannot say the side is +/-20 m as the side cannot be -20
in such cases we say the square root of x^2=absolute value of x
i am sure your teacher meant this

Answer 4

In a purely mathematical sense, the answer is +/-x (positive and negative x) beacuse there are 2 roots.

Any equation with the variable to the second power will have 2 roots (answers).

If the equation has x to the 5th power, there will be 5 roots (answers).

For every-day, real world problems, you can ignore the negative root. But, you can't discount -x as an answer to your question.

Answer 5

It is absolute value of x because -x * -x is x^2 and x * x = x^2.

Answer 6

X^2 is X squared which is X times X (X x X)
so square root is what times itself it the number so square root of X^2 is X since x times itself gives you X^2

Answer 7

square root of x^2=IxI not -x
IXI-MEANS MODULUS OF X
despite
-x*-x=x^2
and
x*x=x^2
as square root refers to the root of positive no.
therefore its given by modx

Answer 8

+/- x or +x (if you are dealing with measurements of real objects - because measurements can't be negative)

Answer 9

x