Simplify. Rationalize the denominator. 10/7 + sqrt 5 ______

Select Conjugate: Select the conjugate of 7 + sqrt(5). Conjugate of a a + sqrt(b): a - sqrt(b) Conjugate of 7 + sqrt(5): 7 - sqrt(5)Multiply by Conjugate: Multiply the original expression by the conjugate over itself to rationalize the denominator. (10/(7 + sqrt(5))) * ((7 - sqrt(5))/(7 - sqrt(5)))Simplify Numerator: Simplify the numerator by distributing the multiplication. 10 * (7 - sqrt(5)) = 70 - 10 * sqrt(5)Simplify Denominator: Simplify the denominator by using the difference of squares formula. (7 + sqrt(5)) * (7 - sqrt(5)) = 7^2 - (sqrt(5))^2 = 49 - 5 = 44Write with Rationalized Denominator: Write the simplified expression with the rationalized denominator. (70 - 10 * sqrt(5)) / 44Simplify Numerator and Denominator: Simplify the expression by dividing both terms in the numerator by the denominator. 70/44 - (10 * sqrt(5))/44Reduce Fractions: Reduce the fractions to their simplest form if possible. 70/44 = 35/22 and (10 * sqrt(5))/44 = (5 * sqrt(5))/22Write Final Expression: Write the final simplified expression. (35/22) - (5 * sqrt(5))/22

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Simplify. Rationalize the denominator. $\newline$ $\frac{10}{7 + \sqrt{5}}$

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Algebra 2

Simplify radical expressions using conjugates

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Q. Simplify. Rationalize the denominator.

\newline

\frac{10}{7 + \sqrt{5}}

Select Conjugate: Select the conjugate of $7 + \sqrt{5}$ . $\newline$ Conjugate of $a + \sqrt{b}$ : $a - \sqrt{b}$ $\newline$ Conjugate of $7 + \sqrt{5}$ : $7 - \sqrt{5}$
Multiply by Conjugate: Multiply the original expression by the conjugate over itself to rationalize the denominator. $\newline$ $(\frac{10}{7 + \sqrt{5}}) \cdot \frac{7 - \sqrt{5}}{7 - \sqrt{5}}$
Simplify Numerator: Simplify the numerator by distributing the multiplication. $\newline$ $10 \times (7 - \sqrt{5}) = 70 - 10 \times \sqrt{5}$
Simplify Denominator: Simplify the denominator by using the difference of squares formula. $\newline$ $(7 + \sqrt{5}) \times (7 - \sqrt{5}) = 7^2 - (\sqrt{5})^2 = 49 - 5 = 44$
Write with Rationalized Denominator: Write the simplified expression with the rationalized denominator. $(70 - 10 \cdot \sqrt{5}) / 44$
Simplify Numerator and Denominator: Simplify the expression by dividing both terms in the numerator by the denominator. $\frac{70}{44} - \frac{(10 \cdot \sqrt{5})}{44}$
Reduce Fractions: Reduce the fractions to their simplest form if possible. $\newline$ $\frac{70}{44} = \frac{35}{22}$ and $\frac{10 \cdot \sqrt{5}}{44} = \frac{5 \cdot \sqrt{5}}{22}$
Write Final Expression: Write the final simplified expression. $\frac{35}{22} - \frac{5 \cdot \sqrt{5}}{22}$