Rationalizing Radicals Worksheet

Rationalizing Radicals

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: \(\frac{1}{2 + \sqrt{3}}\)

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

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

6. When rationalizing a binomial denominator of the form \(a + \sqrt{b}\), you multiply by its  , which is \(a - \sqrt{b}\).

7. Which of the following is the rationalized form of \(\frac{4}{\sqrt{8}}\)?

8. Rationalize the denominator: \(\frac{1}{\sqrt{x} + \sqrt{y}}\)