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

Find Conjugate: Select the conjugate of 3 + sqrt(2). Conjugate of a a + sqrt(b): a - sqrt(b) Conjugate of 3 + sqrt(2): 3 - sqrt(2)Multiply by Conjugate: Multiply the original expression by the conjugate over itself to rationalize the denominator. 10/(3 + sqrt(2)) * (3 - sqrt(2))/(3 - sqrt(2))Simplify Numerator: Simplify the numerator by distributing the 10 across the conjugate. 10 * (3 - sqrt(2)) = 10 * 3 - 10 * sqrt(2) = 30 - 10 * sqrt(2)Simplify Denominator: Simplify the denominator by using the difference of squares formula. (3 + sqrt(2)) * (3 - sqrt(2)) = 3^2 - (sqrt(2))^2 = 9 - 2 = 7Write Simplified Expression: Write the simplified expression with the rationalized denominator. (30 - 10 * sqrt(2))/7 This fraction is already in simplest form.

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

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Algebra 2

Simplify radical expressions using conjugates

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Q. Simplify. Rationalize the denominator.

\newline

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

Find Conjugate: Select the conjugate of $3 + \sqrt{2}$ . $\newline$ Conjugate of $a + \sqrt{b}$ : $a - \sqrt{b}$ $\newline$ Conjugate of $3 + \sqrt{2}$ : $3 - \sqrt{2}$
Multiply by Conjugate: Multiply the original expression by the conjugate over itself to rationalize the denominator. $\newline$ $\frac{10}{3 + \sqrt{2}} \cdot \frac{3 - \sqrt{2}}{3 - \sqrt{2}}$
Simplify Numerator: Simplify the numerator by distributing the $10$ across the conjugate. $10 \times (3 - \sqrt{2})$ = $10 \times 3 - 10 \times \sqrt{2}$ = $30 - 10 \times \sqrt{2}$
Simplify Denominator: Simplify the denominator by using the difference of squares formula. $\newline$ $(3 + \sqrt{2}) \times (3 - \sqrt{2})$ $\newline$ $= 3^2 - (\sqrt{2})^2$ $\newline$ $= 9 - 2$ $\newline$ $= 7$
Write Simplified Expression: Write the simplified expression with the rationalized denominator. $\newline$ $(30 - 10 \cdot \sqrt{2})/7$ $\newline$ This fraction is already in simplest form.