Simplify square root of x^2+4x+4

$\sqrt{x^{2} + 4 x + 4}$

Step 1

Factor using the perfect square rule.

Rewrite $4$ as $2^{2}$ .

$\sqrt{x^{2} + 4 x + 2^{2}}$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$4 x = 2 \cdot x \cdot 2$

Rewrite the polynomial.

$\sqrt{x^{2} + 2 \cdot x \cdot 2 + 2^{2}}$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = x$ and $b = 2$ .

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

Step 2

Pull terms out from under the radical, assuming positive real numbers.

$x + 2$