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

Select Conjugate: Select the conjugate of -2 - sqrt(2). Conjugate of a - sqrt(b): a + sqrt(b) Conjugate of -2 - sqrt(2): -2 + sqrt(2)Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator to rationalize it. 5/(-2 - sqrt(2)) * (-2 + sqrt(2))/(-2 + sqrt(2))Simplify Numerator: Simplify the numerator by distributing the 5 across the conjugate. 5 * (-2 + sqrt(2)) = 5 * (-2) + 5 * (sqrt(2)) = -10 + 5sqrt(2)Simplify Denominator: Simplify the denominator by using the difference of squares formula. (-2 - sqrt(2)) * (-2 + sqrt(2)) = (-2)^2 - (sqrt(2))^2 = 4 - 2 = 2Combine Numerator and Denominator: Combine the simplified numerator and denominator. (-10 + 5sqrt(2))/2 This fraction is already in simplest form.

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

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Algebra 2

Simplify radical expressions using conjugates

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Q. Simplify. Rationalize the denominator.

\newline

\frac{5}{-2 - \sqrt{2}}

Select Conjugate: Select the conjugate of $-2 - \sqrt{2}$ . $\newline$ Conjugate of $a - \sqrt{b}$ : $a + \sqrt{b}$ $\newline$ Conjugate of $-2 - \sqrt{2}$ : $-2 + \sqrt{2}$
Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator to rationalize it. $\newline$ $\frac{5}{-2 - \sqrt{2}} \times \frac{-2 + \sqrt{2}}{-2 + \sqrt{2}}$
Simplify Numerator: Simplify the numerator by distributing the $5$ across the conjugate. $5 \times (-2 + \sqrt{2})$ = $5 \times (-2) + 5 \times (\sqrt{2})$ = $-10 + 5\sqrt{2}$
Simplify Denominator: Simplify the denominator by using the difference of squares formula. $\newline$ $(-2 - \sqrt{2}) * (-2 + \sqrt{2})$ $\newline$ $= (-2)^2 - (\sqrt{2})^2$ $\newline$ $= 4 - 2$ $\newline$ $= 2$
Combine Numerator and Denominator: Combine the simplified numerator and denominator. $\newline$ $(-10 + 5\sqrt{2})/2$ $\newline$ This fraction is already in simplest form.