Why is square root of (x-1)^2 not...

[anniev2]

OG 11 # 171

If (x-1)^2 = 400, which of the following could be the value of x-5?

(A) 15
(B) 14
(C) -24
(D) -25
(E) -26

OA is C


Why is square root of (x-1)^2 not equal to -(x-1) and (x-1). I thought that taking the square root of a number means its +/- the number. Please advise.

[cramya]

Know this: Square root of x^2 = |x|

(x-1) ^ 2 = 400

|x-1| = 20

Case 1: x is positive

x-1 = 20
x=21

Case 2: x is negative

-(x-1)= 20

-x+1 = 20

x=-19




x-1 could have equaled 21 or -19

(21-1)^2 = 400 and (-19-1)^2 = 400


-19-5= -24 -> the only choice given since 21-5 = 16 is not one of the choices

Hence C

Regards,
CR

[logitech]

well this problem is like:
'
X^2=400 and the two cases you need to consider is on the right side of the equation:

+20 and - 20

I am sure you can solve the question now.