Expanding Brackets with Surds
This worksheet focuses on expanding algebraic expressions involving surds (radicals) by applying the distributive property and simplifying the results. Suitable for Grade 10 math students.
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Expanding Brackets with Surds
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Expand the following expressions involving surds and simplify your answers where possible. Remember to use the distributive property.
1. Expand and simplify: \( \sqrt{3}(2 + \sqrt{3}) \)
2. Expand and simplify: \( \sqrt{5}(\sqrt{10} - 3) \)
3. Fill in the blanks to complete the expansion: \( \sqrt{2}(4 - \sqrt{8}) = 4\sqrt{2} - \sqrt{ } = 4\sqrt{2} - \)
4. Fill in the blanks to complete the expansion: \( 2\sqrt{3}(\sqrt{6} + \sqrt{3}) = 2\sqrt{ } + 2\sqrt{ } = 2\sqrt{18} + 2(3) = 2(3\sqrt{2}) + 6 = + 6 \)
5. Expand and simplify: \( (2 + \sqrt{3})(1 + \sqrt{3}) \)
6. Expand and simplify: \( (\sqrt{5} - 2)(\sqrt{5} + 3) \)
7. Which of the following is the correct expansion and simplification of \( (\sqrt{7} + 1)(\sqrt{7} - 1) \)?
\( 7 - \sqrt{7} \)
\( 6 \)
\( 7 \)
\( 8 \)
8. Expand and simplify: \( (3\sqrt{2} - \sqrt{5})^2 \)
9. Expand and simplify: \( (\sqrt{x} + \sqrt{y})(\sqrt{x} - \sqrt{y}) \)