Simplify. Rationalize the denominator. 3/-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 2Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator to rationalize it. 3/(-2 + sqrt 2) * (-2 - sqrt 2)/(-2 - sqrt 2)Simplify Numerator: Simplify the numerator by distributing 3 to both terms in the conjugate. 3 * (-2) - 3 * (sqrt 2) = -6 - 3sqrt(2)Simplify Denominator: Simplify the denominator by using the difference of squares formula: (a - b)(a + b) = a^2 - b^2. (-2 + sqrt 2) * (-2 - sqrt 2) = (-2)^2 - (sqrt 2)^2 = 4 - 2 = 2Combine Numerator and Denominator: Combine the simplified numerator and denominator. (-6 - 3sqrt(2))/2 This fraction is already in simplest form.

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Simplify. Rationalize the denominator. $\newline$ $\frac{3}{-2 + \sqrt{2}}$

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Algebra 2

Simplify radical expressions using conjugates

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Q. Simplify. Rationalize the denominator.

\newline

\frac{3}{-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. $\newline$ $\frac{3}{-2 + \sqrt{2}} \cdot \frac{-2 - \sqrt{2}}{-2 - \sqrt{2}}$
Simplify Numerator: Simplify the numerator by distributing $3$ to both terms in the conjugate. $\newline$ $3 \times (-2) - 3 \times (\sqrt{2})$ $\newline$ = $-6 - 3\sqrt{2}$
Simplify Denominator: Simplify the denominator by using the difference of squares formula: $(a - b)(a + b) = a^2 - b^2$ . $(-2 + \sqrt{2}) * (-2 - \sqrt{2})$ $= (-2)^2 - (\sqrt{2})^2$ $= 4 - 2$ $= 2$
Combine Numerator and Denominator: Combine the simplified numerator and denominator. $\newline$ $(-6 - 3\sqrt{2})/2$ $\newline$ This fraction is already in simplest form.