How do you simplify: square root of (x^2 - 4x +4)?

1 Answer
Jul 19, 2015

Answer:

#sqrt(x^2-4x+4) = sqrt((x-2)^2) = abs(x-2)#

Explanation:

Note that #x^2-4x+4 = (x-2)^2# has two square roots,
namely #(x-2)# and #-(x-2)#.

Since we use #sqrt# to denote the positive square root, we need to pick whichever is non-negative of #(x-2)# and #-(x-2)#.

We can express that as #abs(x-2)#