Question
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
Upstudy AI Solution
Tutor-Verified Answer
Answer
\(\frac{\sqrt{35}}{5}\)
Solution
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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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: \[ \frac{\sqrt{35}}{5} \]