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Racionaliza el denominador * (3 Points) \( \frac{2}{\sqrt{7}} \) \( \frac{\sqrt{7}}{7} \) \( \frac{\sqrt{7}}{6} \) \( \frac{\sqrt{6}}{7} \) \( \frac{2 \sqrt{7}}{7} \)

Ask by Deleon Hodges. in Puerto Rico
Jan 23,2025

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Answer

To rationalize the denominator of \( \frac{2}{\sqrt{7}} \), multiply numerator and denominator by \( \sqrt{7} \): \[ \frac{2}{\sqrt{7}} \times \frac{\sqrt{7}}{\sqrt{7}} = \frac{2\sqrt{7}}{7} \] So, the correct answer is \( \frac{2 \sqrt{7}}{7} \).

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The Deep Dive

¡Aventurémonos en el emocionante mundo de la racionalización de denominadores! Para racionalizar \( \frac{2}{\sqrt{7}} \), simplemente multiplicamos tanto el numerador como el denominador por \( \sqrt{7} \). Esto simplifica nuestra fracción a \( \frac{2 \sqrt{7}}{7} \). ¡Listo! Hemos eliminado la raíz del denominador. Ahora, es importante recordar que muchos cometen el error de simplemente 'cancelar' las raíces sin multiplicar correctamente y mantener la fracción equilibrada. Asegúrate siempre de multiplicar por la forma adecuada de uno para que el valor de la expresión no cambie y se mantenga correcto. ¡Practica esto y dominarás la racionalización!

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