Simplify ( square root of 13+x)^2

${(\sqrt{13} + x)}^{2}$

Step 1

Rewrite ${(\sqrt{13} + x)}^{2}$ as $(\sqrt{13} + x) (\sqrt{13} + x)$ .

$(\sqrt{13} + x) (\sqrt{13} + x)$

Step 2

Expand $(\sqrt{13} + x) (\sqrt{13} + x)$ using the FOIL Method.

Apply the distributive property.

$\sqrt{13} (\sqrt{13} + x) + x (\sqrt{13} + x)$

Apply the distributive property.

$\sqrt{13} \sqrt{13} + \sqrt{13} x + x (\sqrt{13} + x)$

Apply the distributive property.

$\sqrt{13} \sqrt{13} + \sqrt{13} x + x \sqrt{13} + x \cdot x$

Step 3

Simplify and combine like terms.

Simplify each term.

Combine using the product rule for radicals.

$\sqrt{13 \cdot 13} + \sqrt{13} x + x \sqrt{13} + x \cdot x$

Multiply $13$ by $13$ .

$\sqrt{169} + \sqrt{13} x + x \sqrt{13} + x \cdot x$

Rewrite $169$ as $13^{2}$ .

$\sqrt{13^{2}} + \sqrt{13} x + x \sqrt{13} + x \cdot x$

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

$13 + \sqrt{13} x + x \sqrt{13} + x \cdot x$

Multiply $x$ by $x$ .

$13 + \sqrt{13} x + x \sqrt{13} + x^{2}$

Reorder the factors of $\sqrt{13} x$ .

$13 + x \sqrt{13} + x \sqrt{13} + x^{2}$

Add $x \sqrt{13}$ and $x \sqrt{13}$ .

$13 + 2 x \sqrt{13} + x^{2}$