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

Find Conjugate: Select the conjugate of -8 - sqrt(3). Conjugate of a - sqrt(b): a + sqrt(b) Conjugate of -8 - sqrt(3): -8 + sqrt(3)Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator. Which expression can be used to rationalize the denominator? Multiply (-8 + sqrt(3)) with 2, and -8 - sqrt(3). (2 * (-8 + sqrt(3)))/((-8 - sqrt(3)) * (-8 + sqrt(3)))Simplify Numerator: Simplify the numerator: 2 * (-8 + sqrt(3)) 2 * (-8) + 2 * (sqrt(3)) = -16 + 2sqrt(3)Simplify Denominator: Simplify the denominator: (-8 - sqrt(3)) * (-8 + sqrt(3)) Using the difference of squares formula: (a - b)(a + b) = a^2 - b^2 (-8)^2 - (sqrt(3))^2 = 64 - 3 = 61Combine Numerator and Denominator: Combine the simplified numerator and denominator. (-16 + 2sqrt(3))/61 This fraction is already in simplest form.

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

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Algebra 2

Simplify radical expressions using conjugates

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Q. Simplify. Rationalize the denominator.

\newline

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

Find Conjugate: Select the conjugate of $-8 - \sqrt{3}$ . $\newline$ Conjugate of $a - \sqrt{b}$ : $a + \sqrt{b}$ $\newline$ Conjugate of $-8 - \sqrt{3}$ : $-8 + \sqrt{3}$
Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator. $\newline$ Which expression can be used to rationalize the denominator? $\newline$ Multiply $(-8 + \sqrt{3})$ with $2$ , and $-8 - \sqrt{3}$ . $\newline$ $\frac{2 \cdot (-8 + \sqrt{3})}{(-8 - \sqrt{3}) \cdot (-8 + \sqrt{3})}$
Simplify Numerator: Simplify the numerator: $2 \times (-8 + \sqrt{3})$ $\newline$ $2 \times (-8) + 2 \times (\sqrt{3})$ $\newline$ $= -16 + 2\sqrt{3}$
Simplify Denominator: Simplify the denominator: $(-8 - \sqrt{3}) * (-8 + \sqrt{3})$ $\newline$ Using the difference of squares formula: $(a - b)(a + b) = a^2 - b^2$ $\newline$ $(-8)^2 - (\sqrt{3})^2$ $\newline$ $= 64 - 3$ $\newline$ $= 61$
Combine Numerator and Denominator: Combine the simplified numerator and denominator. $\newline$ $(-16 + 2\sqrt{3})/61$ $\newline$ This fraction is already in simplest form.