Simplify (x+ square root of 3)^2

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

Step 1

Rewrite ${(x + \sqrt{3})}^{2}$ as $(x + \sqrt{3}) (x + \sqrt{3})$ .

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

Step 2

Expand $(x + \sqrt{3}) (x + \sqrt{3})$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

$x \cdot x + x \sqrt{3} + \sqrt{3} (x + \sqrt{3})$

Apply the distributive property.

$x \cdot x + x \sqrt{3} + \sqrt{3} x + \sqrt{3} \sqrt{3}$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \sqrt{3} + \sqrt{3} x + \sqrt{3} \sqrt{3}$

Combine using the product rule for radicals.

$x^{2} + x \sqrt{3} + \sqrt{3} x + \sqrt{3 \cdot 3}$

Multiply $3$ by $3$ .

$x^{2} + x \sqrt{3} + \sqrt{3} x + \sqrt{9}$

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

$x^{2} + x \sqrt{3} + \sqrt{3} x + \sqrt{3^{2}}$

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

$x^{2} + x \sqrt{3} + \sqrt{3} x + 3$

Reorder the factors of $\sqrt{3} x$ .

$x^{2} + x \sqrt{3} + x \sqrt{3} + 3$

Add $x \sqrt{3}$ and $x \sqrt{3}$ .

$x^{2} + 2 x \sqrt{3} + 3$