Rationalizing the Denominator Worksheet

Rationalizing the Denominator

Carefully rationalize the denominator for each expression. Show all your work for full credit.

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

2. Rationalize the denominator: \(\frac{2\sqrt{3}}{\sqrt{7}}\)

3. Rationalize the denominator: \(\frac{1}{2\sqrt{6}}\)

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

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

6. Rationalize the denominator: \(\frac{\sqrt{3} + 1}{\sqrt{3} - 1}\)

7. Rationalize the denominator: \(\frac{1}{\sqrt[3]{2}}\)

8. Rationalize the denominator: \(\frac{4}{\sqrt[3]{9}}\)

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

10. To rationalize a denominator of the form \(a + \sqrt{b}\), multiply both the numerator and denominator by its  , which is \(a - \sqrt{b}\).