Simplify (7- square root of 3)(-6+ square root of 3)

$(7 - \sqrt{3}) (- 6 + \sqrt{3})$

Step 1

Expand $(7 - \sqrt{3}) (- 6 + \sqrt{3})$ using the FOIL Method.

Apply the distributive property.

$7 (- 6 + \sqrt{3}) - \sqrt{3} (- 6 + \sqrt{3})$

Apply the distributive property.

$7 \cdot - 6 + 7 \sqrt{3} - \sqrt{3} (- 6 + \sqrt{3})$

Apply the distributive property.

$7 \cdot - 6 + 7 \sqrt{3} - \sqrt{3} \cdot - 6 - \sqrt{3} \sqrt{3}$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $7$ by $- 6$ .

$- 42 + 7 \sqrt{3} - \sqrt{3} \cdot - 6 - \sqrt{3} \sqrt{3}$

Multiply $- 6$ by $- 1$ .

$- 42 + 7 \sqrt{3} + 6 \sqrt{3} - \sqrt{3} \sqrt{3}$

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

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

$- 42 + 7 \sqrt{3} + 6 \sqrt{3} - ({\sqrt{3}}^{1} \sqrt{3})$

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

$- 42 + 7 \sqrt{3} + 6 \sqrt{3} - ({\sqrt{3}}^{1} {\sqrt{3}}^{1})$

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

$- 42 + 7 \sqrt{3} + 6 \sqrt{3} - {\sqrt{3}}^{1 + 1}$

Add $1$ and $1$ .

$- 42 + 7 \sqrt{3} + 6 \sqrt{3} - {\sqrt{3}}^{2}$

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

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

$- 42 + 7 \sqrt{3} + 6 \sqrt{3} - {(3^{\frac{1}{2}})}^{2}$

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

$- 42 + 7 \sqrt{3} + 6 \sqrt{3} - 3^{\frac{1}{2} \cdot 2}$

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

$- 42 + 7 \sqrt{3} + 6 \sqrt{3} - 3^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$- 42 + 7 \sqrt{3} + 6 \sqrt{3} - 3^{\frac{2}{2}}$

Rewrite the expression.

$- 42 + 7 \sqrt{3} + 6 \sqrt{3} - 3^{1}$

Evaluate the exponent.

$- 42 + 7 \sqrt{3} + 6 \sqrt{3} - 1 \cdot 3$

Multiply $- 1$ by $3$ .

$- 42 + 7 \sqrt{3} + 6 \sqrt{3} - 3$

Subtract $3$ from $- 42$ .

$- 45 + 7 \sqrt{3} + 6 \sqrt{3}$

Add $7 \sqrt{3}$ and $6 \sqrt{3}$ .

$- 45 + 13 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 45 + 13 \sqrt{3}$

Decimal Form:

$- 22.48333950 \dots$

Simplify (7- square root of 3)(-6+ square root of 3)

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