Simplify. Rationalize the denominator. 6/-10 - sqrt 5 ______

Find Conjugate: Select the conjugate of -10 - sqrt(5). Conjugate of a - sqrt(b): a + sqrt(b) Conjugate of -10 - sqrt(5): -10 + sqrt(5)Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator. To rationalize the denominator, we multiply the fraction by (-10 + sqrt(5))/(-10 + sqrt(5)). 6/(-10 - sqrt(5)) * (-10 + sqrt(5))/(-10 + sqrt(5))Simplify Numerator: Simplify the numerator by distributing the 6. 6 * (-10 + sqrt(5)) = 6 * (-10) + 6 * sqrt(5) = -60 + 6 * sqrt(5)Simplify Denominator: Simplify the denominator using the difference of squares formula. (-10 - sqrt(5)) * (-10 + sqrt(5)) = (-10)^2 - (sqrt(5))^2 = 100 - 5 = 95Write Simplified Fraction: Write the simplified fraction. (-60 + 6 * sqrt(5))/95 This fraction is already in simplest form.

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Simplify. Rationalize the denominator. $\newline$ $\frac{6}{-10 - \sqrt{5}}$

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Algebra 2

Simplify radical expressions using conjugates

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Q. Simplify. Rationalize the denominator.

\newline

\frac{6}{-10 - \sqrt{5}}

Find Conjugate: Select the conjugate of $-10 - \sqrt{5}$ . $\newline$ Conjugate of $a - \sqrt{b}$ : $a + \sqrt{b}$ $\newline$ Conjugate of $-10 - \sqrt{5}$ : $-10 + \sqrt{5}$
Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator. $\newline$ To rationalize the denominator, we multiply the fraction by (-10 + \sqrt{5})/(-10 + \sqrt{5})$\newline$. $\newline$ $\frac{6}{-10 - \sqrt{5}} \times \frac{-10 + \sqrt{5}}{-10 + \sqrt{5}}$
Simplify Numerator: Simplify the numerator by distributing the $6$ . $6 \times (-10 + \sqrt{5})$ $= 6 \times (-10) + 6 \times \sqrt{5}$ $= -60 + 6 \times \sqrt{5}$
Simplify Denominator: Simplify the denominator using the difference of squares formula. $\newline$ $(-10 - \sqrt{5}) * (-10 + \sqrt{5})$ $\newline$ = $(-10)^2 - (\sqrt{5})^2$ $\newline$ = $100 - 5$ $\newline$ = $95$
Write Simplified Fraction: Write the simplified fraction. $(-60 + 6 \times \sqrt{5})/95$ This fraction is already in simplest form.