SOLUTION: What is the square root of x^2 +4x+4 Please explain how to solve it

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Question 230444: What is the square root of x^2 +4x+4 Please explain how to solve it
Found 3 solutions by user_dude2008, Earlsdon, josmiceli:
Answer by user_dude2008(1862) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt(x^2+4x+4)=sqrt((x+2)(x+2))=sqrt( (x+2)^2 ) = |x+2|

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Find the square root:
sqrt%28x%5E2%2B4x%2B4%29 First, factor the trinomial.
sqrt%28%28x%2B2%29%28x%2B2%29%29%29 Notice that %28x%2B2%29%28x%2B2%29+=+%28x%2B2%29%5E2 so substitute.
sqrt%28%28x%2B2%29%29%5E2 and, of course, sqrt%28x%5E2%29+=+x, so sqrt%28%28x%2B2%29%29%5E2+=+x%2B2 and...
highlight%28sqrt%28x%5E2%2B4x%2B4%29+=+x%2B2%29

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
When you ask "What is the square root?" you are
asking "What, multiplied by itself gives me a
certain quantity?"
I need to find smething that if multiplied by itself
gives me x%5E2+%2B+4x+%2B+4
The factors of this equation are of the form
x+-+r%5B1%5D and
x+-+r%5B2%5D
Where r%5B1%5D and r%5B2%5D are the roots
If r%5B1%5D+=+r%5B2%5D, then
%28x+-+r%29%5E2+=+x%5E2+%2B+4x+%2B+4
and x-r is the square root
I'll do the squaring on the left side
x%5E2+-+2rx+%2B+r%5E2+=+x%5E2+%2B+4x+%2B+4
I can just match up coefficients
(1) -2r+=+4
(2) r%5E2+=+4
From (1),
r+=+-2
From (2)
%28-2%29%5E2+=+4
4+=+4
If r+=+-2, then
%28x+-+r%29%5E2+=+x%5E2+%2B+4x+%2B+4
%28x+-+%28-2%29%29%5E2+=+x%5E2+%2B+4x+%2B+4
%28x+%2B+2%29%5E2+=+x%5E2+%2B+4x+%2B+4
and, the square root of the
equation is x+%2B+2 answer