Simplify square root of 18x+18+ square root of 2x+2

$\sqrt{18 x + 18} + \sqrt{2 x + 2}$

Step 1

Simplify each term.

Factor $18$ out of $18 x + 18$ .

Factor $18$ out of $18 x$ .

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

Factor $18$ out of $18$ .

$\sqrt{18 (x) + 18 (1)} + \sqrt{2 x + 2}$

Factor $18$ out of $18 (x) + 18 (1)$ .

$\sqrt{18 (x + 1)} + \sqrt{2 x + 2}$

Rewrite $18 (x + 1)$ as $3^{2} \cdot (2 (x + 1^{2}))$ .

Factor $9$ out of $18$ .

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

Rewrite $9$ as $3^{2}$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

One to any power is one.

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

Factor $2$ out of $2 x + 2$ .

Factor $2$ out of $2 x$ .

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

Factor $2$ out of $2$ .

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

Factor $2$ out of $2 (x) + 2 (1)$ .

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

Step 2

Add $3 \sqrt{2 (x + 1)}$ and $\sqrt{2 (x + 1)}$ .

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