Powers

vladmire wrote:How is k^2=4 suff. can the answer be 2 or -2?

Absolute value is nothing but DISTANCE to 0


-2 ------------------ 0 -------------------- + 2

As you can see both -2 and + 2 are '2' units far away from 0

Think it like your house is 0 and you are walking. If you are 2 miles away from home, you can any where around your house.

So you never say I am -2 miles away from home because you are walking from the opposite way to home.

Good analogy Logitech!.
Crudely put, absolute has NO direction but only magnitude --- a scalar.

Vladimire,
One that should go to your flashcards is

sqrt(k^2) = |k|

Stmt I

k^2 = 4

Take sqrt on both sides

sqrt(k^2) = sqrt(2^2) OR sqrt(k^2) = sqrt(-2^2)

Either way |k| = 2

i.e k can be 2 or -2 but |k| is always 2

Hence SUFF



Some additional notes that may be helpful:

|x| is never negative

By defnition:

If x is positive or 0 then |x| = x

If x is neagtive then |x| = -x (negative(negative) = positive here x is negative)

Eg:

Let x=-2


|x| = |-2| by defnition = - x = - (- 2) = 2