Simplify. Rationalize the denominator. 4/-2 - sqrt 3 ______

Select Conjugate: Select the conjugate of -2 - sqrt(3). Conjugate of a - sqrt(b): a + sqrt(b) Conjugate of -2 - sqrt(3): -2 + sqrt(3)Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator to rationalize it. Expression: (4/(-2 - sqrt(3))) * ((-2 + sqrt(3))/(-2 + sqrt(3)))Multiply Numerator: Perform the multiplication in the numerator. Numerator: 4 * (-2 + sqrt(3)) = 4 * -2 + 4 * sqrt(3) = -8 + 4sqrt(3)Multiply Denominator: Perform the multiplication in the denominator using the difference of squares formula. Denominator: (-2 - sqrt(3)) * (-2 + sqrt(3)) = (-2)^2 - (sqrt(3))^2 = 4 - 3 = 1Write Simplified Expression: Write the simplified expression. Since the denominator is now 1, the expression simplifies to the numerator. Final expression: -8 + 4sqrt(3)

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Simplify. Rationalize the denominator. $\newline$ $\frac{4}{-2 - \sqrt{3}}$

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Algebra 1

Simplify radical expressions using conjugates

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Q. Simplify. Rationalize the denominator.

\newline

\frac{4}{-2 - \sqrt{3}}

Select Conjugate: Select the conjugate of $-2 - \sqrt{3}$ . $\newline$ Conjugate of $a - \sqrt{b}$ : $a + \sqrt{b}$ $\newline$ Conjugate of $-2 - \sqrt{3}$ : $-2 + \sqrt{3}$
Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator to rationalize it. $\newline$ Expression: $(\frac{4}{-2 - \sqrt{3}}) \cdot (\frac{-2 + \sqrt{3}}{-2 + \sqrt{3}})$
Multiply Numerator: Perform the multiplication in the numerator. $\newline$ Numerator: $4 \times (-2 + \sqrt{3})$ $\newline$ = $4 \times -2 + 4 \times \sqrt{3}$ $\newline$ = $-8 + 4\sqrt{3}$
Multiply Denominator: Perform the multiplication in the denominator using the difference of squares formula. $\newline$ Denominator: $(-2 - \sqrt{3}) \times (-2 + \sqrt{3})$ $\newline$ $= (-2)^2 - (\sqrt{3})^2$ $\newline$ $= 4 - 3$ $\newline$ $= $1$
Write Simplified Expression: Write the simplified expression.$\newline$Since the denominator is now $1$, the expression simplifies to the numerator.$\newline$Final expression: $-8 + 4\sqrt{3}$