to get rid of radicals in the denominator of a fraction, you should rationalize the denominator by multiplying the fraction by a helpful form of

To get rid of radicals in the denominator of a fraction, you should rationalize the denominator by multiplying the fraction by a helpful form of **1** that involves the conjugate of the denominator.

### Here's how you can do it:

1. **Identify the radical in the denominator**: For example, if the denominator is \(\sqrt{a}\), you'll need to multiply by \(\frac{\sqrt{a}}{\sqrt{a}}\).

2. **Multiply both the numerator and denominator** by the conjugate of the denominator if it's a binomial: If the denominator is a binomial expression like \(a + \sqrt{b}\), multiply the fraction by \(\frac{a - \sqrt{b}}{a - \sqrt{b}}\). This uses the difference of squares to eliminate the radical.

### Example:
Given the fraction \(\frac{3}{\sqrt{5}}\):

- Multiply both numerator and denominator by \(\sqrt{5}\):  
\[
\frac{3}{\sqrt{5}} \times \frac{\sqrt{5}}{\sqrt{5}} = \frac{3\sqrt{5}}{5}
\]
Now, the denominator is rationalized.

### Key Steps:
1. Identify the radical or binomial in the denominator.
2. Multiply by the conjugate if necessary.
3. Simplify the fraction.

Would you like a detailed explanation of this process, or do you have any other questions?

### Relative Questions:
1. How do you rationalize a denominator with a binomial radical, such as \(1 / (2 + \sqrt{3})\)?
2. What is the difference of squares and how is it used in rationalizing denominators?
3. Can you rationalize a denominator with multiple radicals, like \(\sqrt{2} + \sqrt{3}\)?
4. How do you handle rationalizing a denominator when the numerator also contains a radical?
5. What are some common mistakes to avoid when rationalizing denominators?

### Tip:
Always simplify the fraction after rationalizing the denominator to ensure it's in its simplest form.

Learn how to rationalize the denominator of a fraction with radicals using the conjugate method. Detailed steps and examples provided for effective understanding. Suitable for Grades 9-12.

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