https://file.aiquickdraw.com/mathbot/file/1727110262444hj1wlc22.jpg

To simplify the quotient \(\frac{\sqrt{6}}{\sqrt{13}}\), we can use the property of square roots:

\[
\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}
\]

Applying this property to the given expression:

\[
\frac{\sqrt{6}}{\sqrt{13}} = \sqrt{\frac{6}{13}}
\]

Thus, the simplified form is \(\sqrt{\frac{6}{13}}\). However, none of the given answer choices matches this exact form.

Let's analyze the options provided:

- **A**: \(\frac{6}{\sqrt{78}}\) — This does not simplify correctly from \(\frac{\sqrt{6}}{\sqrt{13}}\).
- **B**: \(\frac{6}{13}\) — This is incorrect, as we cannot remove the square roots like that.
- **C**: \(\frac{\sqrt{6}}{13}\) — Incorrect because it leaves out the square root of 13 in the denominator.
- **D**: \(\frac{\sqrt{78}}{13}\) — Incorrect transformation.

The correct simplification is not reflected in any of the options, but if we were to approximate \(\sqrt{\frac{6}{13}}\), the closest answer might be **C**.

Would you like more details or further clarification?

Here are some related questions:
1. What is the property of square roots used to simplify fractions?
2. How do we simplify \(\frac{\sqrt{a}}{\sqrt{b}}\)?
3. What are the steps to rationalize the denominator when simplifying radicals?
4. Why is \(\frac{\sqrt{6}}{13}\) not the correct simplified form?
5. How can square roots be expressed in decimal form?

**Tip:** Always check if the expression can be simplified before comparing it to the answer options!

Simplify the quotient \(\frac{\sqrt{6}}{\sqrt{13}}\).

Learn how to simplify the radical expression \(\frac{\sqrt{6}}{\sqrt{13}}\) using the property of square roots. Follow the step-by-step process to understand how to apply these properties to fraction simplifications.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation