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

Select Conjugate: Select the conjugate of -10 + sqrt 5. Conjugate of a - sqrt(b): a + sqrt(b) Conjugate of -10 + sqrt 5: -10 - sqrt 5Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator. Which expression can be used to rationalize the denominator? Multiply (-10 - sqrt 5) with 10, and -10 + sqrt 5. (10 * (-10 - sqrt 5))/((-10 + sqrt 5) * (-10 - sqrt 5))Simplify Numerator: Simplify the numerator: 10 * (-10 - sqrt 5) 10 * (-10) - 10 * (sqrt 5) = -100 - 10 * sqrt(5)Simplify Denominator: Simplify the denominator: (-10 + sqrt 5) * (-10 - sqrt 5) (-10)^2 - (sqrt 5)^2 = 100 - 5 = 95Combine Numerator and Denominator: Combine the simplified numerator and denominator. (-100 - 10 * sqrt(5)) / 95 This fraction is already in simplest form.

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

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Algebra 2

Simplify radical expressions using conjugates

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Q. Simplify. Rationalize the denominator.

\newline

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

Select Conjugate: Select the conjugate of $-10 + \sqrt{5}$ . $\newline$ Conjugate of $a - \sqrt{b}$ : $a + \sqrt{b}$ $\newline$ Conjugate of $-10 + \sqrt{5}$ : $-10 - \sqrt{5}$
Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator. $\newline$ Which expression can be used to rationalize the denominator? $\newline$ Multiply $(-10 - \sqrt{5})$ with $10$ , and $-10 + \sqrt{5}$ . $\newline$ $\frac{10 \cdot (-10 - \sqrt{5})}{(-10 + \sqrt{5}) \cdot (-10 - \sqrt{5})}$
Simplify Numerator: Simplify the numerator: $10 \times (-10 - \sqrt{5})$ $\newline$ $10 \times (-10) - 10 \times (\sqrt{5})$ $\newline$ $= -100 - 10 \times \sqrt{5}$
Simplify Denominator: Simplify the denominator: $(-10 + \sqrt{5}) * (-10 - \sqrt{5})$ $\newline$ $(-10)^2 - (\sqrt{5})^2$ $\newline$ $= 100 - 5$ $\newline$ $= $95$
Combine Numerator and Denominator: Combine the simplified numerator and denominator.$\newline$$(-100 - 10 \cdot \sqrt{5}) / 95$$\newline$This fraction is already in simplest form.