Rationalizing the Denominator Worksheet
This worksheet provides practice problems for rationalizing the denominator of expressions involving square roots and cube roots, suitable for Grade 9 algebra students.
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Rationalizing the Denominator
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Rationalize the denominator for each expression. Show all your work.
Simplify the following expressions by rationalizing the denominator.
1. $ \frac{1}{\sqrt{3}} $
2. $ \frac{5}{\sqrt{10}} $
3. $ \frac{2\sqrt{3}}{\sqrt{6}} $
Rationalize the denominator for expressions with binomial denominators.
4. $ \frac{1}{2 + \sqrt{3}} $
5. $ \frac{4}{\sqrt{5} - \sqrt{2}} $
6. $ \frac{\sqrt{3} + 1}{\sqrt{3} - 1} $
Rationalize the denominator for expressions involving cube roots.
7. $ \frac{1}{\sqrt[3]{2}} $
8. $ \frac{5}{\sqrt[3]{4}} $
Complete the following statements.
9. To rationalize a denominator with a single square root, multiply the numerator and denominator by the .
10. The conjugate of $ a + \sqrt{b} $ is .
Indicate whether each statement is True or False.
11. The expression $ \frac{1}{\sqrt{2}} $ is considered rationalized.
True
False
12. Multiplying by the conjugate is a method used to rationalize binomial denominators.
True
False