https://file.aiquickdraw.com/mathbot/file/1727058310660j9uy3lqu.jpg

The problem shown in the image asks to rationalize the expression \(\frac{4}{\sqrt{3}}\).

### Steps to Rationalize:

1. **Multiply the numerator and denominator by \(\sqrt{3}\)**:
   \[
   \frac{4}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{4\sqrt{3}}{(\sqrt{3})^2}
   \]

2. **Simplify**:
   Since \((\sqrt{3})^2 = 3\), the expression becomes:
   \[
   \frac{4\sqrt{3}}{3}
   \]

Thus, the rationalized form of \(\frac{4}{\sqrt{3}}\) is:
\[
\frac{4\sqrt{3}}{3}
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you rationalize an expression with a cube root in the denominator?
2. What is the significance of rationalizing the denominator in mathematics?
3. How would you rationalize \(\frac{5}{\sqrt{2}}\)?
4. Can the numerator also contain a square root during rationalization?
5. How would you handle the rationalization if the denominator had a binomial expression like \(1 + \sqrt{2}\)?

**Tip:** When rationalizing the denominator, multiplying by the conjugate is useful if there is a binomial expression like \(a + \sqrt{b}\).

Rationalize the expression \(\frac{4}{\sqrt{3}}\).

Learn how to rationalize the expression \(\frac{4}{\sqrt{3}}\) with step-by-step instructions. This tutorial covers key algebraic concepts, including multiplying by the square root and simplifying radicals. Ideal 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