How do you simplify $\sqrt{9 x^{2} + 18 x + 9}$ $sqrt(9x^2 + 18x + 9)$ ?

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Answer 1 · 2016-02-03T12:35:07

$3 (x + 1)$ $3(x+1)$

1. Factor out 9.

$\sqrt{9 x^{2} + 18 x + 9}$ $sqrt(9x^2+18x+9)$

$= \sqrt{9 (x^{2} + 2 x + 1)}$ $=sqrt(9(x^2+2x+1)$

2. Factor the polynomial.

$= \sqrt{9 {(x + 1)}^{2}}$ $=sqrt(9(x+1)^2)$

3. Simplify.
Recall that $\sqrt{x} = x^{\frac{1}{2}}$ $sqrt(x)=x^(1/2)$ .

$= 9^{\frac{1}{2}} \cdot {({(x + 1)}^{2})}^{\frac{1}{2}}$ $=9^(1/2)*((x+1)^2)^(1/2)$

$= 3 \cdot (x + 1)$ $=3*(x+1)$

$= 3 (x + 1)$ $=3(x+1)$

Answer 2 · 2016-02-03T16:23:30

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

Given $\sqrt{9 x^{2} + 18 x + 9}$ $" "sqrt(9x^2+18x+9)$

but $9 x^{2} + 18 x + 9 = (3 x + 3) (3 x + 3) = {(3 x + 3)}^{2}$ $" " 9x^2+18x+9 = (3x+3)(3x+3) =(3x+3)^2$

so $\sqrt{9 x^{2} + 18 x + 9} = \sqrt{{(3 x + 3)}^{2}}$ $" "sqrt(9x^2+18x+9) = sqrt((3x+3)^2)$

so $\sqrt{9 x^{2} + 18 x + 9} = (3 x + 3)$ $" "sqrt(9x^2+18x+9) = (3x+3)$

How do you simplify √9x2+18x+9sqrt(9x^2 + 18x + 9)?