Rationalizing the Denominator Worksheet
This worksheet provides practice on rationalizing the denominator for expressions involving square roots and cube roots, suitable for Grade 10 Algebra students.
Includes
Standards
Topics
Rationalizing the Denominator
Name:
Date:
Score:
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: \(\frac{\sqrt{x} + \sqrt{y}}{\sqrt{x} - \sqrt{y}}\)