Simplify. Rationalize the denominator. 7/-8 + sqrt 5 ______

Find Conjugate: Select the conjugate of -8 + sqrt 5. Conjugate of a - sqrt(b): a + sqrt(b) Conjugate of -8 + sqrt 5: -8 - sqrt 5Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator. To rationalize the denominator, we multiply the expression by (-8 - sqrt 5)/(-8 - sqrt 5). (7 * (-8 - sqrt 5))/((-8 + sqrt 5) * (-8 - sqrt 5))Simplify Numerator: Simplify the numerator by distributing the 7. 7 * (-8) - 7 * (sqrt 5) = -56 - 7 * sqrt(5)Simplify Denominator: Simplify the denominator using the difference of squares formula. (-8)^2 - (sqrt 5)^2 = 64 - 5 = 59Write Simplified Expression: Write the simplified expression. (-56 - 7 * sqrt(5)) / 59 This fraction is already in simplest form.

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Simplify. Rationalize the denominator. $\newline$ $\frac{7}{-8 + \sqrt{5}}$

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Algebra 2

Simplify radical expressions using conjugates

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Q. Simplify. Rationalize the denominator.

\newline

\frac{7}{-8 + \sqrt{5}}

Find Conjugate: Select the conjugate of $-8 + \sqrt{5}$ . $\newline$ Conjugate of $a - \sqrt{b}$ : $a + \sqrt{b}$ $\newline$ Conjugate of $-8 + \sqrt{5}$ : $-8 - \sqrt{5}$
Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator. $\newline$ To rationalize the denominator, we multiply the expression by (-8 - \sqrt{5})/(-8 - \sqrt{5})$\newline$. $\newline$ $(7 \cdot (-8 - \sqrt{5}))/((-8 + \sqrt{5}) \cdot (-8 - \sqrt{5}))$
Simplify Numerator: Simplify the numerator by distributing the $7$ . $7 \times (-8) - 7 \times (\sqrt{5}) = -56 - 7 \times \sqrt{5}$
Simplify Denominator: Simplify the denominator using the difference of squares formula. $\newline$ $(-8)^2 - (\sqrt{5})^2$ $\newline$ = $64$ - $5$ $\newline$ = $59$
Write Simplified Expression: Write the simplified expression. $(-56 - 7 \sqrt{5}) / 59$ This fraction is already in simplest form.