Simplify ( square root of 6+x)^2

${(\sqrt{6} + x)}^{2}$

Step 1

Rewrite ${(\sqrt{6} + x)}^{2}$ as $(\sqrt{6} + x) (\sqrt{6} + x)$ .

$(\sqrt{6} + x) (\sqrt{6} + x)$

Step 2

Expand $(\sqrt{6} + x) (\sqrt{6} + x)$ using the FOIL Method.

Apply the distributive property.

$\sqrt{6} (\sqrt{6} + x) + x (\sqrt{6} + x)$

Apply the distributive property.

$\sqrt{6} \sqrt{6} + \sqrt{6} x + x (\sqrt{6} + x)$

Apply the distributive property.

$\sqrt{6} \sqrt{6} + \sqrt{6} x + x \sqrt{6} + x \cdot x$

Step 3

Simplify and combine like terms.

Simplify each term.

Combine using the product rule for radicals.

$\sqrt{6 \cdot 6} + \sqrt{6} x + x \sqrt{6} + x \cdot x$

Multiply $6$ by $6$ .

$\sqrt{36} + \sqrt{6} x + x \sqrt{6} + x \cdot x$

Rewrite $36$ as $6^{2}$ .

$\sqrt{6^{2}} + \sqrt{6} x + x \sqrt{6} + x \cdot x$

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

$6 + \sqrt{6} x + x \sqrt{6} + x \cdot x$

Multiply $x$ by $x$ .

$6 + \sqrt{6} x + x \sqrt{6} + x^{2}$

Reorder the factors of $\sqrt{6} x$ .

$6 + x \sqrt{6} + x \sqrt{6} + x^{2}$

Add $x \sqrt{6}$ and $x \sqrt{6}$ .

$6 + 2 x \sqrt{6} + x^{2}$