Question

so (sqrt(x))^2 = abs(x) the reason is that that square part will make it a positive no matter what the inside is?
also does this then mean sqrt(x^2) = x since the ^2 is not on the outside?

Answer 1

\[\sqrt{x}^{2} = \left| x \right|\]

Answer 2

correct

Answer 3

if x <0 then (sqrt(x))^2 != abs(x) as left hand side is -ve but RHS is +ve

Answer 4

\[\sqrt{x ^{2}} = x\]

Answer 5

not always. imagine if x = -1

Answer 6

so this is true when x >= 0

Answer 7

things can get strange when in the world of powers

example

1 = (-1)^(2/10) = (-1)^(1/5) = -1

Answer 8

so when x<0 then x=x ?

Answer 9

I guess it depends on if you take the square root first or wquare it first

sqrt((-1)^2) = sqrt(1) = 1

Answer 10

my calculator says sqrt((-1)^2) = 1

but it says (-1)^(2/2) = -1 so go figure...

Answer 11

well the top part is = to 1 and the bottom part is like wtf lol calculators get tricked ez

Answer 12

not ti-89s

explain this then

1 = (-1)^(2/10) = (-1)^(1/5) = -1

there is more to powers than we are tought in normal math class. some sort of order of operations...