Pregunta
Rationalize the denominator. Simplify the answer. \( \frac{\sqrt{7}}{\sqrt{5}} \) \( \frac{\sqrt{7}}{\sqrt{5}}=\square \) (Type an exact answer using radicals as needed.)
Ask by Fleming John. in the United States
Mar 12,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
\(\frac{\sqrt{35}}{5}\)
Solución
1. Multiply the given expression by \( \frac{\sqrt{5}}{\sqrt{5}} \) to eliminate the radical in the denominator:
\[
\frac{\sqrt{7}}{\sqrt{5}} \times \frac{\sqrt{5}}{\sqrt{5}} = \frac{\sqrt{7} \cdot \sqrt{5}}{\sqrt{5} \cdot \sqrt{5}}
\]
2. Simplify the numerator and the denominator:
- The numerator becomes \( \sqrt{7 \times 5} = \sqrt{35} \).
- The denominator becomes \( \sqrt{5 \times 5} = \sqrt{25} = 5 \).
3. Write the final simplified expression:
\[
\frac{\sqrt{35}}{5}
\]
\(\frac{\sqrt{7}}{\sqrt{5}} = \frac{\sqrt{35}}{5}\)
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Como
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Extra Insights
To rationalize the denominator of \( \frac{\sqrt{7}}{\sqrt{5}} \), we multiply both the numerator and the denominator by \( \sqrt{5} \): \[ \frac{\sqrt{7}}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}} = \frac{\sqrt{7} \cdot \sqrt{5}}{5} = \frac{\sqrt{35}}{5} \] So, the simplified answer is: \[ \frac{\sqrt{35}}{5} \]

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