Rationalizing Radicals Worksheet
A Grade 12 math worksheet on rationalizing radicals, including simplifying expressions and solving problems.
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Rationalizing Radicals
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Read each question carefully and rationalize the radical expressions. Show all your work for full credit.
1. To rationalize a denominator with a single square root, multiply the numerator and denominator by .
2. The conjugate of \( a + \sqrt{b} \) is .
3. Rationalize the denominator: \( \frac{5}{\sqrt{7}} \)
4. Simplify and rationalize: \( \frac{1}{2 + \sqrt{3}} \)
5. Which of the following is the rationalized form of \( \frac{\sqrt{2}}{\sqrt{6} - \sqrt{3}} \)?
\( \frac{\sqrt{12} + \sqrt{6}}{3} \)
\( \frac{2 + \sqrt{3}}{3} \)
\( \frac{\sqrt{12} - \sqrt{6}}{3} \)
\( \frac{2 - \sqrt{3}}{3} \)
6. Rationalize the denominator: \( \frac{4}{\sqrt{x} - 2} \)
7. Simplify and rationalize: \( \frac{\sqrt{a} + \sqrt{b}}{\sqrt{a} - \sqrt{b}} \)
8. The expression \( \frac{1}{\sqrt[3]{2}} \) can be rationalized by multiplying the numerator and denominator by \( \sqrt[3]{2} \).
True
False