Simplify (4- square root of 3)^2

${(4 - \sqrt{3})}^{2}$

Step 1

Rewrite ${(4 - \sqrt{3})}^{2}$ as $(4 - \sqrt{3}) (4 - \sqrt{3})$ .

$(4 - \sqrt{3}) (4 - \sqrt{3})$

Step 2

Expand $(4 - \sqrt{3}) (4 - \sqrt{3})$ using the FOIL Method.

Apply the distributive property.

$4 (4 - \sqrt{3}) - \sqrt{3} (4 - \sqrt{3})$

Apply the distributive property.

$4 \cdot 4 + 4 (- \sqrt{3}) - \sqrt{3} (4 - \sqrt{3})$

Apply the distributive property.

$4 \cdot 4 + 4 (- \sqrt{3}) - \sqrt{3} \cdot 4 - \sqrt{3} (- \sqrt{3})$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $4$ by $4$ .

$16 + 4 (- \sqrt{3}) - \sqrt{3} \cdot 4 - \sqrt{3} (- \sqrt{3})$

Multiply $- 1$ by $4$ .

$16 - 4 \sqrt{3} - \sqrt{3} \cdot 4 - \sqrt{3} (- \sqrt{3})$

Multiply $4$ by $- 1$ .

$16 - 4 \sqrt{3} - 4 \sqrt{3} - \sqrt{3} (- \sqrt{3})$

Multiply $- \sqrt{3} (- \sqrt{3})$ .

Multiply $- 1$ by $- 1$ .

$16 - 4 \sqrt{3} - 4 \sqrt{3} + 1 \sqrt{3} \sqrt{3}$

Multiply $\sqrt{3}$ by $1$ .

$16 - 4 \sqrt{3} - 4 \sqrt{3} + \sqrt{3} \sqrt{3}$

Raise $\sqrt{3}$ to the power of $1$ .

$16 - 4 \sqrt{3} - 4 \sqrt{3} + {\sqrt{3}}^{1} \sqrt{3}$

Raise $\sqrt{3}$ to the power of $1$ .

$16 - 4 \sqrt{3} - 4 \sqrt{3} + {\sqrt{3}}^{1} {\sqrt{3}}^{1}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$16 - 4 \sqrt{3} - 4 \sqrt{3} + {\sqrt{3}}^{1 + 1}$

Add $1$ and $1$ .

$16 - 4 \sqrt{3} - 4 \sqrt{3} + {\sqrt{3}}^{2}$

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$16 - 4 \sqrt{3} - 4 \sqrt{3} + {(3^{\frac{1}{2}})}^{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$16 - 4 \sqrt{3} - 4 \sqrt{3} + 3^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

$16 - 4 \sqrt{3} - 4 \sqrt{3} + 3^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$16 - 4 \sqrt{3} - 4 \sqrt{3} + 3^{\frac{2}{2}}$

Rewrite the expression.

$16 - 4 \sqrt{3} - 4 \sqrt{3} + 3^{1}$

Evaluate the exponent.

$16 - 4 \sqrt{3} - 4 \sqrt{3} + 3$

Add $16$ and $3$ .

$19 - 4 \sqrt{3} - 4 \sqrt{3}$

Subtract $4 \sqrt{3}$ from $- 4 \sqrt{3}$ .

$19 - 8 \sqrt{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$19 - 8 \sqrt{3}$

Decimal Form:

$5.14359353 \dots$

Simplify (4- square root of 3)^2

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