What is the square root of: #x^2 + 4x + 4#?

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Answer 1 · 2018-04-29T22:25:17

The square root equals #x+2#.

First, factor the expression under the radical:

#color(white)=sqrt(x^2+4x+4)#

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

#=sqrt(color(red)x(x+2)+2x+4)#

#=sqrt(color(red)x(x+2)+color(blue)2(x+2))#

#=sqrt((color(red)x+color(blue)2)(x+2))#

#=sqrt((x+2)^2)#

#=x+2#

That's the simplification. Hope this helped!