Simplify. Rationalize the denominator. 5/-6 - sqrt 3 ______

Find Conjugate: Select the conjugate of -6 - sqrt(3). The conjugate of a - sqrt(b) is a + sqrt(b). So, the conjugate of -6 - sqrt(3) is -6 + sqrt(3).Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator. To rationalize the denominator, we multiply the numerator and the denominator by the conjugate of the denominator. So, we multiply 5/(-6 - sqrt(3)) by (-6 + sqrt(3))/(-6 + sqrt(3)).Multiply Numerator: Apply the multiplication to the numerator. Multiply 5 by (-6 + sqrt(3)). 5 * (-6 + sqrt(3)) = -30 + 5sqrt(3)Multiply Denominator: Apply the multiplication to the denominator. Multiply (-6 - sqrt(3)) by (-6 + sqrt(3)). This is a difference of squares which is (a - b)(a + b) = a^2 - b^2. So, (-6)^2 - (sqrt(3))^2 = 36 - 3 = 33.Write Simplified Expression: Write the simplified expression. Now we have (-30 + 5sqrt(3))/33. This fraction is already in simplest form.

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Simplify. Rationalize the denominator. $\newline$ $\frac{5}{-6 - \sqrt{3}}$

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Algebra 2

Simplify radical expressions using conjugates

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Q. Simplify. Rationalize the denominator.

\newline

\frac{5}{-6 - \sqrt{3}}

Find Conjugate: Select the conjugate of $-6 - \sqrt{3}$ . $\newline$ The conjugate of $a - \sqrt{b}$ is $a + \sqrt{b}$ . $\newline$ So, the conjugate of $-6 - \sqrt{3}$ is $-6 + \sqrt{3}$ .
Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator. $\newline$ To rationalize the denominator, we multiply the numerator and the denominator by the conjugate of the denominator. $\newline$ So, we multiply $\frac{5}{-6 - \sqrt{3}}$ by $\frac{-6 + \sqrt{3}}{-6 + \sqrt{3}}$ .
Multiply Numerator: Apply the multiplication to the numerator. $\newline$ Multiply $5$ by $(-6 + \sqrt{3})$ . $\newline$ $5 \times (-6 + \sqrt{3}) = -30 + 5\sqrt{3}$
Multiply Denominator: Apply the multiplication to the denominator. $\newline$ Multiply $(-6 - \sqrt{3})$ by $(-6 + \sqrt{3})$ . $\newline$ This is a difference of squares which is $(a - b)(a + b) = a^2 - b^2$ . $\newline$ So, $(-6)^2 - (\sqrt{3})^2 = 36 - 3 = 33$ .
Write Simplified Expression: Write the simplified expression. $\newline$ Now we have $(-30 + 5\sqrt{3})/33$ . $\newline$ This fraction is already in simplest form.