Simplify ( square root of 2+x)^2

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

Step 1

Rewrite ${(\sqrt{2} + x)}^{2}$ as $(\sqrt{2} + x) (\sqrt{2} + x)$ .

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

Step 2

Expand $(\sqrt{2} + x) (\sqrt{2} + x)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Combine using the product rule for radicals.

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

Multiply $2$ by $2$ .

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

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

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

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

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

Multiply $x$ by $x$ .

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

Reorder the factors of $\sqrt{2} x$ .

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

Add $x \sqrt{2}$ and $x \sqrt{2}$ .

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