How do you simplify #sqrt(9x^2 + 18x + 9)#?

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Answer 1 · 2016-02-03T12:35:07

#3(x+1)#

1. Factor out 9.

#sqrt(9x^2+18x+9)#

#=sqrt(9(x^2+2x+1)#

2. Factor the polynomial.

#=sqrt(9(x+1)^2)#

3. Simplify.
Recall that #sqrt(x)=x^(1/2)#.

#=9^(1/2)*((x+1)^2)^(1/2)#

#=3*(x+1)#

#=3(x+1)#

Answer 2 · 2016-02-03T16:23:30

#3x+3" " # slightly different approach!

Given#" "sqrt(9x^2+18x+9)#

but #" " 9x^2+18x+9 = (3x+3)(3x+3) =(3x+3)^2#

so #" "sqrt(9x^2+18x+9) = sqrt((3x+3)^2)#

so #" "sqrt(9x^2+18x+9) = (3x+3)#