Rationalizing the Denominator
A Grade 11 math worksheet focusing on rationalizing the denominator, including expressions with square roots and binomial denominators.
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Rationalizing the Denominator
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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 \(\frac{4}{\sqrt{7} + 1}\)?
\(\frac{4(\sqrt{7} - 1)}{6}\)
\(\frac{4(\sqrt{7} + 1)}{6}\)
\(\frac{2(\sqrt{7} - 1)}{3}\)
\(\frac{2(\sqrt{7} + 1)}{3}\)
8. Rationalize the denominator: \(\frac{x - y}{\sqrt{x} - \sqrt{y}}\)