Expanding Brackets with Surds
This worksheet focuses on expanding algebraic expressions involving surds, covering fundamental and advanced techniques for Grade 11 students.
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Expanding Brackets with Surds
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Expand and simplify the following expressions involving surds. Remember to rationalize denominators where necessary.
1. Expand and simplify: \(\sqrt{2}(3 + \sqrt{8})\)
2. Expand and simplify: \(\sqrt{5}(\sqrt{10} - 2)\)
3. Complete the expansion: \((2 + \sqrt{3})(4 - \sqrt{3}) = 8 - 2\sqrt{3} + 4\sqrt{3} - \sqrt{9} = 8 + - 3 = \)
4. Expand and simplify: \((5 - \sqrt{2})(1 + \sqrt{2}) = \)
5. Expand and simplify: \((3 + \sqrt{5})^2\)
6. Expand and simplify: \((\sqrt{7} - 2)^2\)
7. Which of the following is the simplified form of \((\sqrt{6} + \sqrt{2})(\sqrt{6} - \sqrt{2})\)?
8
4
4\(\sqrt{6}\)
2\(\sqrt{6}\)
8. Expand and simplify: \((2\sqrt{3} + 1)(3\sqrt{3} - 2)\)
9. Expand and simplify: \((4 - \sqrt{x})(4 + \sqrt{x})\)