Question
Rationalize the denominator. \( \frac{\sqrt{7}}{\sqrt{5}} \)
Ask by Lang Whittaker. in the United States
Jan 22,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
To rationalize the denominator of \( \frac{\sqrt{7}}{\sqrt{5}} \), multiply numerator and denominator by \( \sqrt{5} \), resulting in \( \frac{\sqrt{35}}{5} \).
Solution
To rationalize the denominator of the expression \( \frac{\sqrt{7}}{\sqrt{5}} \), follow these steps:
1. **Multiply the numerator and the denominator by \( \sqrt{5} \):**
\[
\frac{\sqrt{7}}{\sqrt{5}} \times \frac{\sqrt{5}}{\sqrt{5}} = \frac{\sqrt{7} \times \sqrt{5}}{\sqrt{5} \times \sqrt{5}}
\]
2. **Simplify the expression:**
- **Numerator:** \( \sqrt{7} \times \sqrt{5} = \sqrt{35} \)
- **Denominator:** \( \sqrt{5} \times \sqrt{5} = 5 \)
So, the expression becomes:
\[
\frac{\sqrt{35}}{5}
\]
**Final Answer:**
\[
\frac{\sqrt{35}}{5}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To rationalize the denominator of \( \frac{\sqrt{7}}{\sqrt{5}} \), you can multiply both the numerator and denominator by \( \sqrt{5} \). This gives you: \[ \frac{\sqrt{7} \cdot \sqrt{5}}{\sqrt{5} \cdot \sqrt{5}} = \frac{\sqrt{35}}{5} \] Now, the expression \( \frac{\sqrt{35}}{5} \) has a rational denominator, making it neater and easier to work with in further calculations. Next, remember that when rationalizing, it's a great idea to check if you can simplify the numerator. In this case, \( \sqrt{35} \) is already in its simplest form, so you're all set! Rationalizing can help avoid complications in further mathematical operations and is essential in many proofs.
