Simplify. Rationalize the denominator. 8/-2 - sqrt 3 ______

Select Conjugate: Select the conjugate of -2 - sqrt 3. Conjugate of a - sqrt(b): a + sqrt(b) Conjugate of -2 - sqrt 3: -2 + sqrt 3Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator to rationalize it. (8) / (-2 - sqrt 3) * (-2 + sqrt 3) / (-2 + sqrt 3)Apply Distributive Property: Apply the distributive property to multiply the numerators and the denominators. Numerator: 8 * (-2 + sqrt 3) = 8 * -2 + 8 * sqrt 3 = -16 + 8sqrt(3) Denominator: (-2 - sqrt 3) * (-2 + sqrt 3) = (-2)^2 - (sqrt(3))^2 = 4 - 3Simplify Denominator: Simplify the denominator. 4 - 3 = 1Final Answer: Since the denominator is now 1, the simplified form of the expression is just the numerator. Final Answer: -16 + 8sqrt(3)

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Simplify. Rationalize the denominator. $\newline$ $\frac{8}{-2 - \sqrt{3}}$

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Algebra 1

Simplify radical expressions using conjugates

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Q. Simplify. Rationalize the denominator.

\newline

\frac{8}{-2 - \sqrt{3}}

Select Conjugate: Select the conjugate of $-2 - \sqrt{3}$ . $\newline$ Conjugate of $a - \sqrt{b}$ : $a + \sqrt{b}$ $\newline$ Conjugate of $-2 - \sqrt{3}$ : $-2 + \sqrt{3}$
Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator to rationalize it. $\newline$ $(8) / (-2 - \sqrt{3}) \cdot (-2 + \sqrt{3}) / (-2 + \sqrt{3})$
Apply Distributive Property: Apply the distributive property to multiply the numerators and the denominators. $\newline$ Numerator: $8 \times (-2 + \sqrt{3}) = 8 \times -2 + 8 \times \sqrt{3} = -16 + 8\sqrt{3}$ $\newline$ Denominator: $(-2 - \sqrt{3}) \times (-2 + \sqrt{3}) = (-2)^2 - (\sqrt{3})^2 = 4 - 3$
Simplify Denominator: Simplify the denominator. $4 - 3 = 1$
Final Answer: Since the denominator is now $1$ , the simplified form of the expression is just the numerator. $\newline$ Final Answer: $-16 + 8\sqrt{3}$