Simplify. Rationalize the denominator. 10/-8 + sqrt 3 ______

Select Conjugate: Select the conjugate of -8 + sqrt 3. Conjugate of a - sqrt(b): a + sqrt(b) Conjugate of -8 + sqrt 3: -8 - sqrt 3Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator. To rationalize the denominator, we multiply the fraction by (-8 - sqrt 3)/(-8 - sqrt 3). (10/(-8 + sqrt 3)) * ((-8 - sqrt 3)/(-8 - sqrt 3))Simplify Numerator: Simplify the numerator by distributing the multiplication. 10 * (-8 - sqrt 3) = 10 * (-8) - 10 * (sqrt 3) = -80 - 10 sqrt 3Simplify Denominator: Simplify the denominator using the difference of squares formula. (-8 + sqrt 3) * (-8 - sqrt 3) = (-8)^2 - (sqrt 3)^2 = 64 - 3 = 61Write Simplified Expression: Write the simplified expression. (-80 - 10 sqrt 3)/61 This fraction is already in simplest form.

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Simplify. Rationalize the denominator. $\newline$ $\frac{10}{-8 + \sqrt{3}}$

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Algebra 2

Simplify radical expressions using conjugates

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Q. Simplify. Rationalize the denominator.

\newline

\frac{10}{-8 + \sqrt{3}}

Select 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. $\newline$ To rationalize the denominator, we multiply the fraction by (-8 - \sqrt{3})/(-8 - \sqrt{3})$\newline$. $\newline$ $(10/(-8 + \sqrt{3})) \times ((-8 - \sqrt{3})/(-8 - \sqrt{3}))$
Simplify Numerator: Simplify the numerator by distributing the multiplication. $\newline$ $10 \times (-8 - \sqrt{3})$ $\newline$ = $10 \times (-8) - 10 \times (\sqrt{3})$ $\newline$ = $-80 - 10\sqrt{3}$
Simplify Denominator: Simplify the denominator using the difference of squares formula. $\newline$ $(-8 + \sqrt{3}) * (-8 - \sqrt{3})$ $\newline$ $= (-8)^2 - (\sqrt{3})^2$ $\newline$ $= 64 - 3$ $\newline$ $= 61$
Write Simplified Expression: Write the simplified expression. $\newline$ $(-80 - 10 \sqrt{3})/61$ $\newline$ This fraction is already in simplest form.