To simplify the expression \( \frac{3}{4\sqrt{6}} \), we can follow these steps:

1. **Rationalize the denominator**: Multiply both the numerator and denominator by \( \sqrt{6} \) to eliminate the square root in the denominator.
   \[
   \frac{3}{4\sqrt{6}} \times \frac{\sqrt{6}}{\sqrt{6}} = \frac{3\sqrt{6}}{4 \times 6} = \frac{3\sqrt{6}}{24}
   \]

2. **Simplify the fraction**: Now, reduce the fraction by dividing both the numerator and the denominator by 3:
   \[
   \frac{3\sqrt{6}}{24} = \frac{\sqrt{6}}{8}
   \]

Thus, the simplified form of \( \frac{3}{4\sqrt{6}} \) is \( \frac{\sqrt{6}}{8} \).

Would you like further details on this process or any questions?

Here are five related questions:
1. How do you rationalize a denominator with higher powers of square roots?
2. What is the general method for simplifying fractions with radicals?
3. How would you simplify \( \frac{5}{\sqrt{3}} \)?
4. Can you rationalize a denominator in more complex fractions involving cubes?
5. What are some common mistakes when rationalizing denominators?

**Tip:** Always ensure to simplify your final expression as much as possible after rationalizing the denominator.

Learn how to simplify the expression \( \frac{3}{4\sqrt{6}} \) by rationalizing the denominator and reducing the fraction. This step-by-step solution covers key algebraic concepts and techniques, such as rationalizing radicals and simplifying fractions. Suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation