Multiplying Radicals Worksheet
Practice multiplying radical expressions, including simplifying and rationalizing denominators, suitable for Grade 12 Algebra students.
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Multiplying Radicals
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Read each question carefully and show all your work. Simplify all radical expressions to their simplest form. Rationalize all denominators where necessary.
1. Multiply and simplify: \( \sqrt{3} \cdot \sqrt{12} \)
2. Multiply and simplify: \( 2\sqrt{5} \cdot 3\sqrt{10} \)
3. Expand and simplify: \( \sqrt{2}(\sqrt{8} + \sqrt{18}) \) =
4. Expand and simplify: \( 4\sqrt{3}(2\sqrt{6} - \sqrt{3}) \) =
5. Multiply and simplify: \( (\sqrt{7} + 2)(\sqrt{7} - 2) \)
6. Multiply and simplify: \( (2\sqrt{3} + 5)( \sqrt{3} - 1) \)
7. Rationalize the denominator and simplify: \( \frac{6}{\sqrt{3}} \)
\( 2\sqrt{3} \)
\( \frac{6\sqrt{3}}{3} \)
\( \frac{\sqrt{3}}{2} \)
\( 6\sqrt{3} \)
8. Rationalize the denominator and simplify: \( \frac{1}{2 + \sqrt{5}} \)
\( 2 - \sqrt{5} \)
\( -2 - \sqrt{5} \)
\( -2 + \sqrt{5} \)
\( \frac{2 + \sqrt{5}}{9} \)
9. Simplify completely: \( (\sqrt{x} + \sqrt{y})(\sqrt{x} - \sqrt{y}) \)
10. Rationalize the denominator: \( \frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} - \sqrt{2}} \)