Simplify. Rationalize the denominator. 10/-6 - sqrt 3 ______

Find Conjugate: Select the conjugate of -6 - sqrt(3). Conjugate of a - sqrt(b): a + sqrt(b) Conjugate of -6 - sqrt(3): -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 expression by (-6 + sqrt(3))/(-6 + sqrt(3)). (10/(-6 - sqrt(3))) * ((-6 + sqrt(3))/(-6 + sqrt(3)))Simplify Numerator: Simplify the numerator by distributing the multiplication. 10 * (-6 + sqrt(3)) = 10 * (-6) + 10 * (sqrt(3)) = -60 + 10sqrt(3)Simplify Denominator: Simplify the denominator using the difference of squares formula. (-6 - sqrt(3)) * (-6 + sqrt(3)) = (-6)^2 - (sqrt(3))^2 = 36 - 3 = 33Write Simplified Expression: Write the simplified expression. (-60 + 10sqrt(3))/33 This fraction is already in simplest form.

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Simplify. Rationalize the denominator. $\newline$ $\frac{10}{-6 - \sqrt{3}}$

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Algebra 2

Simplify radical expressions using conjugates

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Q. Simplify. Rationalize the denominator.

\newline

\frac{10}{-6 - \sqrt{3}}

Find Conjugate: Select the conjugate of $-6 - \sqrt{3}$ . $\newline$ Conjugate of $a - \sqrt{b}$ : $a + \sqrt{b}$ $\newline$ Conjugate of $-6 - \sqrt{3}$ : $-6 + \sqrt{3}$
Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator. $\newline$ To rationalize the denominator, we multiply the expression by (-6 + \sqrt{3})/(-6 + \sqrt{3})$\newline$. $\newline$ $(10/(-6 - \sqrt{3})) \times ((-6 + \sqrt{3})/(-6 + \sqrt{3}))$
Simplify Numerator: Simplify the numerator by distributing the multiplication. $\newline$ $10 \times (-6 + \sqrt{3})$ $\newline$ = $10 \times (-6) + 10 \times (\sqrt{3})$ $\newline$ = $-60 + 10\sqrt{3}$
Simplify Denominator: Simplify the denominator using the difference of squares formula. $\newline$ $(-6 - \sqrt{3}) * (-6 + \sqrt{3})$ $\newline$ = $(-6)^2 - (\sqrt{3})^2$ $\newline$ = $36 - 3$ $\newline$ = $33$
Write Simplified Expression: Write the simplified expression. $(-60 + 10\sqrt{3})/33$ This fraction is already in simplest form.