Simplify ( square root of 7+x)^2

${(\sqrt{7} + x)}^{2}$

Step 1

Rewrite ${(\sqrt{7} + x)}^{2}$ as $(\sqrt{7} + x) (\sqrt{7} + x)$ .

$(\sqrt{7} + x) (\sqrt{7} + x)$

Step 2

Expand $(\sqrt{7} + x) (\sqrt{7} + x)$ using the FOIL Method.

Apply the distributive property.

$\sqrt{7} (\sqrt{7} + x) + x (\sqrt{7} + x)$

Apply the distributive property.

$\sqrt{7} \sqrt{7} + \sqrt{7} x + x (\sqrt{7} + x)$

Apply the distributive property.

$\sqrt{7} \sqrt{7} + \sqrt{7} x + x \sqrt{7} + x \cdot x$

Step 3

Simplify and combine like terms.

Simplify each term.

Combine using the product rule for radicals.

$\sqrt{7 \cdot 7} + \sqrt{7} x + x \sqrt{7} + x \cdot x$

Multiply $7$ by $7$ .

$\sqrt{49} + \sqrt{7} x + x \sqrt{7} + x \cdot x$

Rewrite $49$ as $7^{2}$ .

$\sqrt{7^{2}} + \sqrt{7} x + x \sqrt{7} + x \cdot x$

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

$7 + \sqrt{7} x + x \sqrt{7} + x \cdot x$

Multiply $x$ by $x$ .

$7 + \sqrt{7} x + x \sqrt{7} + x^{2}$

Reorder the factors of $\sqrt{7} x$ .

$7 + x \sqrt{7} + x \sqrt{7} + x^{2}$

Add $x \sqrt{7}$ and $x \sqrt{7}$ .

$7 + 2 x \sqrt{7} + x^{2}$