Expanding Brackets with Surds
This worksheet focuses on expanding brackets involving surds, a key concept in Grade 12 Algebra, covering single and double bracket expansions.
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Expanding Brackets with Surds
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Expand and simplify the following expressions involving surds. Show all your working steps clearly.
1. Expand and simplify: \( \sqrt{3}(2 + \sqrt{3}) \)
2. Expand and simplify: \( \sqrt{5}(\sqrt{10} - 4) \)
3. Expand and simplify: \( 2\sqrt{2}(3\sqrt{2} + \sqrt{8}) \)
4. Expand and simplify: \( (1 + \sqrt{2})(3 + \sqrt{2}) \)
5. Expand and simplify: \( (\sqrt{7} - 2)(\sqrt{7} + 5) \)
6. Expand and simplify: \( (2\sqrt{3} + 1)(\sqrt{3} - 4) \)
7. When expanding \( (a + \sqrt{b})(a - \sqrt{b}) \), the result will always be a number, free from surds.
8. Expand and simplify: \( (5 + \sqrt{3})(5 - \sqrt{3}) \) =
9. Expand and simplify: \( (\sqrt{11} - \sqrt{2})(\sqrt{11} + \sqrt{2}) \) =
10. Which of the following is equivalent to \( (\sqrt{6} + 2)^2 \)?
\( 6 + 4\sqrt{6} + 4 \)
\( 10 + 4\sqrt{6} \)
\( 10 + 2\sqrt{6} \)
\( 36 + 4 \)