Simplify. Rationalize the denominator. 10/-2 + sqrt 3 ______

Question Prompt: Question prompt: How can we simplify the expression and rationalize the denominator of 10/(-2 + sqrt(3))?Select Conjugate: Select the conjugate of -2 + sqrt(3). Conjugate of a number in the form a + sqrt(b) is a - sqrt(b), and vice versa. Conjugate of -2 + sqrt(3) is -2 - sqrt(3).Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator to rationalize it. (10 * (-2 - sqrt(3)))/((-2 + sqrt(3)) * (-2 - sqrt(3)))Simplify Numerator: Simplify the numerator by distributing the multiplication. 10 * (-2) + 10 * (-sqrt(3)) = -20 - 10sqrt(3)Simplify Denominator: Simplify the denominator using the difference of squares formula (a + b)(a - b) = a^2 - b^2. (-2)^2 - (sqrt(3))^2 = 4 - 3 = 1Write Simplified Expression: Write the simplified expression. (-20 - 10sqrt(3))/1 Since dividing by 1 does not change the value, the expression simplifies to: -20 - 10sqrt(3)

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Simplify. Rationalize the denominator. $\newline$ $\frac{10}{-2 + \sqrt{3}}$

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Algebra 2

Simplify radical expressions using conjugates

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Q. Simplify. Rationalize the denominator.

\newline

\frac{10}{-2 + \sqrt{3}}

Question Prompt: Question prompt: How can we simplify the expression and rationalize the denominator of $\frac{10}{-2 + \sqrt{3}}$ ?
Select Conjugate: Select the conjugate of $-2 + \sqrt{3}$ . Conjugate of a number in the form $a + \sqrt{b}$ is $a - \sqrt{b}$ , and vice versa. Conjugate of $-2 + \sqrt{3}$ is $-2 - \sqrt{3}$ .
Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator to rationalize it. $\newline$ $(10 \cdot (-2 - \sqrt{3}))/((-2 + \sqrt{3}) \cdot (-2 - \sqrt{3}))$
Simplify Numerator: Simplify the numerator by distributing the multiplication. $\newline$ $10 \times (-2) + 10 \times (-\sqrt{3})$ $\newline$ = $-20 - 10\sqrt{3}$
Simplify Denominator: Simplify the denominator using the difference of squares formula $(a + b)(a - b) = a^2 - b^2$ . $\newline$ $(-2)^2 - (\sqrt{3})^2$ $\newline$ $= 4 - 3$ $\newline$ $= 1$
Write Simplified Expression: Write the simplified expression. $\newline$ $(-20 - 10\sqrt{3})/1$ $\newline$ Since dividing by $1$ does not change the value, the expression simplifies to: $\newline$ $-20 - 10\sqrt{3}$