Rationalizing the Denominator

Rationalizing the Denominator

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

4. The product of \((\sqrt{a} + \sqrt{b})(\sqrt{a} - \sqrt{b})\) is  .

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

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

7. Which of the following is the rationalized form of \(\frac{4}{\sqrt{7} + 1}\)?

8. Rationalize the denominator: \(\frac{x - y}{\sqrt{x} - \sqrt{y}}\)