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

2 Answers
Feb 3, 2016

Answer:

#3(x+1)#

Explanation:

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)#

Feb 3, 2016

Answer:

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

Explanation:

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)#