Simplify. Rationalize the denominator. 5/5 + sqrt 3 ______

Find Conjugate: Select the conjugate of 5 + sqrt(3). The conjugate of a + sqrt(b) is a - sqrt(b). So, the conjugate of 5 + sqrt(3) is 5 - sqrt(3).Multiply by Conjugate: Multiply the original expression by 1 in the form of the conjugate over itself. To rationalize the denominator, we multiply the numerator and the denominator by the conjugate of the denominator. (5/(5 + sqrt(3))) * ((5 - sqrt(3))/(5 - sqrt(3)))Simplify Numerator: Simplify the numerator. Multiply 5 by the conjugate (5 - sqrt(3)). 5 * (5 - sqrt(3)) = 25 - 5*sqrt(3)Simplify Denominator: Simplify the denominator. Use the difference of squares formula: (a + b)(a - b) = a^2 - b^2. (5 + sqrt(3))(5 - sqrt(3)) = 5^2 - (sqrt(3))^2 = 25 - 3Calculate Denominator: Calculate the denominator. 25 - 3 = 22Write Simplified Expression: Write the simplified expression. (25 - 5*sqrt(3))/22 This fraction is already in simplest form.

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Simplify. Rationalize the denominator. $\newline$ $\frac{5}{5 + \sqrt{3}}$

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Algebra 2

Simplify radical expressions using conjugates

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Q. Simplify. Rationalize the denominator.

\newline

\frac{5}{5 + \sqrt{3}}

Find Conjugate: Select the conjugate of $5 + \sqrt{3}$ . The conjugate of $a + \sqrt{b}$ is $a - \sqrt{b}$ . So, the conjugate of $5 + \sqrt{3}$ is $5 - \sqrt{3}$ .
Multiply by Conjugate: Multiply the original expression by $1$ in the form of the conjugate over itself. $\newline$ To rationalize the denominator, we multiply the numerator and the denominator by the conjugate of the denominator. $\newline$ $\frac{5}{5 + \sqrt{3}}$ * $\frac{5 - \sqrt{3}}{5 - \sqrt{3}}$
Simplify Numerator: Simplify the numerator. $\newline$ Multiply $5$ by the conjugate $(5 - \sqrt{3})$ . $\newline$ $5 \times (5 - \sqrt{3}) = 25 - 5\sqrt{3}$
Simplify Denominator: Simplify the denominator. $\newline$ Use the difference of squares formula: $(a + b)(a - b) = a^2 - b^2$ . $\newline$ $(5 + \sqrt{3})(5 - \sqrt{3}) = 5^2 - (\sqrt{3})^2 = 25 - 3$
Calculate Denominator: Calculate the denominator. $25 - 3 = 22$
Write Simplified Expression: Write the simplified expression. $(25 - 5\sqrt{3})/22$ This fraction is already in simplest form.