Simplify. Rationalize the denominator. 5/-6 + sqrt 2 ______

Select Conjugate: Select the conjugate of -6 + sqrt 2. Conjugate of a - sqrt(b): a + sqrt(b) Conjugate of -6 + sqrt 2: -6 - sqrt 2Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator to rationalize it. 5/(-6 + sqrt 2) multiplied by (-6 - sqrt 2)/(-6 - sqrt 2)Simplify Numerator: Simplify the numerator by distributing the 5 across the conjugate. 5 * (-6 - sqrt 2) = 5 * (-6) - 5 * (sqrt 2) = -30 - 5 * sqrt(2)Simplify Denominator: Simplify the denominator by using the difference of squares formula. (-6 + sqrt 2) * (-6 - sqrt 2) = (-6)^2 - (sqrt 2)^2 = 36 - 2 = 34Combine Numerator and Denominator: Combine the simplified numerator and denominator. (-30 - 5 * sqrt(2)) / 34 This fraction is already in simplest form.

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Simplify. Rationalize the denominator. $\newline$ $\frac{5}{-6 + \sqrt{2}}$

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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{2}}

Select Conjugate: Select the conjugate of $-6 + \sqrt{2}$ . $\newline$ Conjugate of $a - \sqrt{b}$ : $a + \sqrt{b}$ $\newline$ Conjugate of $-6 + \sqrt{2}$ : $-6 - \sqrt{2}$
Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator to rationalize it. $\frac{5}{-6 + \sqrt{2}}$ multiplied by $\frac{-6 - \sqrt{2}}{-6 - \sqrt{2}}$
Simplify Numerator: Simplify the numerator by distributing the $5$ across the conjugate. $5 \times (-6 - \sqrt{2})$ $= 5 \times (-6) - 5 \times (\sqrt{2})$ $= -30 - 5 \times \sqrt{2}$
Simplify Denominator: Simplify the denominator by using the difference of squares formula. $\newline$ $(-6 + \sqrt{2}) * (-6 - \sqrt{2})$ $\newline$ $= (-6)^2 - (\sqrt{2})^2$ $\newline$ $= 36 - 2$ $\newline$ $= 34$
Combine Numerator and Denominator: Combine the simplified numerator and denominator. $\newline$ $(-30 - 5 \cdot \sqrt{2}) / 34$ $\newline$ This fraction is already in simplest form.