Simplify. Rationalize the denominator. 10/-5 + sqrt 2 ______

Select Conjugate: Select the conjugate of -5 + sqrt 2. Conjugate of a - sqrt(b): a + sqrt(b) Conjugate of -5 + sqrt 2: -5 - sqrt 2Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator. To rationalize the denominator, we multiply the expression by (-5 - sqrt 2)/(-5 - sqrt 2). (10/(-5 + sqrt 2)) * ((-5 - sqrt 2)/(-5 - sqrt 2))Simplify Numerator: Simplify the numerator by distributing the multiplication. 10 * (-5 - sqrt 2) = 10 * (-5) + 10 * (-sqrt 2) = -50 - 10sqrt(2)Simplify Denominator: Simplify the denominator using the difference of squares formula. (-5 + sqrt 2) * (-5 - sqrt 2) = (-5)^2 - (sqrt 2)^2 = 25 - 2 = 23Write Simplified Expression: Write the simplified expression. (-50 - 10sqrt(2))/23 This fraction is already in simplest form.

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Simplify. Rationalize the denominator. $\newline$ $\frac{10}{-5 + \sqrt{2}}$

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Algebra 2

Simplify radical expressions using conjugates

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Q. Simplify. Rationalize the denominator.

\newline

\frac{10}{-5 + \sqrt{2}}

Select Conjugate: Select the conjugate of $-5 + \sqrt{2}$ . $\newline$ Conjugate of $a - \sqrt{b}$ : $a + \sqrt{b}$ $\newline$ Conjugate of $-5 + \sqrt{2}$ : $-5 - \sqrt{2}$
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 (-5 - \sqrt{2})/(-5 - \sqrt{2})$\newline$. $\newline$ $(10/(-5 + \sqrt{2})) \times ((-5 - \sqrt{2})/(-5 - \sqrt{2}))$
Simplify Numerator: Simplify the numerator by distributing the multiplication. $\newline$ $10 \times (-5 - \sqrt{2})$ $\newline$ = $10 \times (-5) + 10 \times (-\sqrt{2})$ $\newline$ = $-50 - 10\sqrt{2}$
Simplify Denominator: Simplify the denominator using the difference of squares formula. $\newline$ $(-5 + \sqrt{2}) \times (-5 - \sqrt{2})$ $\newline$ $= (-5)^2 - (\sqrt{2})^2$ $\newline$ $= 25 - 2$ $\newline$ $= 23$
Write Simplified Expression: Write the simplified expression. $\newline$ $(-50 - 10\sqrt{2})/23$ $\newline$ This fraction is already in simplest form.