Simplify the Radical Expression square root of 12x^2+12x+3

$\sqrt{12 x^{2} + 12 x + 3}$

Step 1

Factor $3$ out of $12 x^{2} + 12 x + 3$ .

Factor $3$ out of $12 x^{2}$ .

$\sqrt{3 (4 x^{2}) + 12 x + 3}$

Factor $3$ out of $12 x$ .

$\sqrt{3 (4 x^{2}) + 3 (4 x) + 3}$

Factor $3$ out of $3$ .

$\sqrt{3 (4 x^{2}) + 3 (4 x) + 3 (1)}$

Factor $3$ out of $3 (4 x^{2}) + 3 (4 x)$ .

$\sqrt{3 (4 x^{2} + 4 x) + 3 (1)}$

Factor $3$ out of $3 (4 x^{2} + 4 x) + 3 (1)$ .

$\sqrt{3 (4 x^{2} + 4 x + 1)}$

Step 2

Factor using the perfect square rule.

Rewrite $4 x^{2}$ as ${(2 x)}^{2}$ .

$\sqrt{3 ({(2 x)}^{2} + 4 x + 1)}$

Rewrite $1$ as $1^{2}$ .

$\sqrt{3 ({(2 x)}^{2} + 4 x + 1^{2})}$

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

$4 x = 2 \cdot (2 x) \cdot 1$

Rewrite the polynomial.

$\sqrt{3 ({(2 x)}^{2} + 2 \cdot (2 x) \cdot 1 + 1^{2})}$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = 2 x$ and $b = 1$ .

$\sqrt{3 {(2 x + 1)}^{2}}$

Step 3

Rewrite $3 {(2 x + 1)}^{2}$ as ${(2 x + 1^{2})}^{2} \cdot 3$ .

Reorder $3$ and ${(2 x + 1)}^{2}$ .

$\sqrt{{(2 x + 1)}^{2} \cdot 3}$

Rewrite $1$ as $1^{2}$ .

$\sqrt{{(2 x + 1^{2})}^{2} \cdot 3}$

Step 4

Pull terms out from under the radical.

$| 2 x + 1^{2} | \sqrt{3}$

Step 5

One to any power is one.

$| 2 x + 1 | \sqrt{3}$