Rationalizing the Denominator Worksheet

Rationalizing the Denominator

Read each question carefully and rationalize the denominator for each expression. Show all your work.

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

2. Rationalize the denominator: \(\frac{2\sqrt{3}}{\sqrt{6}}\)

3. Rationalize the denominator: \(\frac{10}{3\sqrt{2}}\)

4. Rationalize the denominator: \(\frac{1}{2 + \sqrt{3}}\)

5. Rationalize the denominator: \(\frac{\sqrt{2}}{\sqrt{5} - \sqrt{3}}\)

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

Indicate whether the following statements are True or False by filling in the blank with T or F.

7. To rationalize \(\frac{1}{\sqrt{a}}\), you multiply both the numerator and denominator by \(\sqrt{a}\).  

8. The conjugate of \(3 - \sqrt{7}\) is \(3 + \sqrt{7}\).  

9. Rationalizing the denominator means removing all radical expressions from the numerator.  

10. Simplify and rationalize the denominator: \(\frac{\sqrt{x} + \sqrt{y}}{\sqrt{x} - \sqrt{y}}\)