SOLUTION: Please help me answer these questions: Rewrite the following square roots when x<-3: 1) {{{sqrt((x-2)^2)}}} The answer I got for this was -(x-2), when x>2 and x-2 when x< or equ

Algebra ->  Inequalities -> SOLUTION: Please help me answer these questions: Rewrite the following square roots when x<-3: 1) {{{sqrt((x-2)^2)}}} The answer I got for this was -(x-2), when x>2 and x-2 when x< or equ      Log On


   

Question 982597: Please help me answer these questions:
Rewrite the following square roots when x<-3:
1) sqrt%28%28x-2%29%5E2%29
The answer I got for this was -(x-2), when x>2 and x-2 when x< or equal to-2 but i'm not sure if this is right.
2) sqrt%28%28x%2B2%29%5E2%29
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28%28%28xLessThanNegThree%29-2%29%5E2%29, the binomial will be a negative number but then still inside the square root function, the binomial is being squared and becomes positive.

Also, understand that abs%28x-2%29=sqrt%28%28x-2%29%5E2%29, and the critical x value is 2. Negative 3 clearly makes x-2%3C0.

abs%28x-2%29 when x-2 is negative becomes abs%28x-2%29=-%28x-2%29=highlight%28-x%2B2%29.


The second equation to analyze will work similarly. x+2 will be negative for x%3C-3.