Rationalizing Radicals Worksheet

Rationalizing Radicals

Read each question carefully and rationalize the radical expressions. Show all your work for full credit.

1. To rationalize a denominator with a single square root, multiply the numerator and denominator by  .

2. The conjugate of \( a + \sqrt{b} \) is  .

3. Rationalize the denominator: \( \frac{5}{\sqrt{7}} \)

4. Simplify and rationalize: \( \frac{1}{2 + \sqrt{3}} \)

5. Which of the following is the rationalized form of \( \frac{\sqrt{2}}{\sqrt{6} - \sqrt{3}} \)?

6. Rationalize the denominator: \( \frac{4}{\sqrt{x} - 2} \)

7. Simplify and rationalize: \( \frac{\sqrt{a} + \sqrt{b}}{\sqrt{a} - \sqrt{b}} \)

8. The expression \( \frac{1}{\sqrt[3]{2}} \) can be rationalized by multiplying the numerator and denominator by \( \sqrt[3]{2} \).