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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

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\(\frac{\sqrt{35}}{5}\)

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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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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