What is the square root of: $x^{2} + 4 x + 4$ $x^2 + 4x + 4$ ?

Question

10222 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-29T22:25:17

The square root equals $x + 2$ $x+2$ .

First, factor the expression under the radical:

$= \sqrt{x^{2} + 4 x + 4}$ $color(white)=sqrt(x^2+4x+4)$

$= \sqrt{x^{2} + 2 x + 2 x + 4}$ $=sqrt(x^2+2x+2x+4)$

$= \sqrt{x (x + 2) + 2 x + 4}$ $=sqrt(color(red)x(x+2)+2x+4)$

$= \sqrt{x (x + 2) + 2 (x + 2)}$ $=sqrt(color(red)x(x+2)+color(blue)2(x+2))$

$= \sqrt{(x + 2) (x + 2)}$ $=sqrt((color(red)x+color(blue)2)(x+2))$

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

$= x + 2$ $=x+2$

That's the simplification. Hope this helped!

What is the square root of: x2+4x+4x^2 + 4x + 4?