Expanding Brackets with Surds
This worksheet focuses on expanding algebraic expressions involving surds, including binomial products and perfect squares, suitable for Grade 9 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 appropriate and simplify all surds to their simplest form.
1. Expand and simplify: \(\sqrt{3} (2 + \sqrt{3})\)
2. Expand and simplify: \(\sqrt{5} (\sqrt{20} - \sqrt{5})\)
3. Expand and simplify: \((2 + \sqrt{3})(1 + \sqrt{3})\) =
4. Expand and simplify: \((\sqrt{7} - 2)(\sqrt{7} + 3)\) =
5. Expand and simplify: \((3\sqrt{2} + 1)(\sqrt{2} - 4)\) =
6. Which of the following is the correct expansion of \((1 + \sqrt{5})^2\)?
\(1 + 5\)
\(1 + 2\sqrt{5} + 5\)
\(1 + \sqrt{5} + 5\)
\(1 + 2\sqrt{5}\)
7. Simplify \((2\sqrt{3} - \sqrt{2})^2\).
\(14 - 4\sqrt{6}\)
\(10\)
\(12 - 2\)
\(12 - 2\sqrt{6} + 2\)
8. The product of \((\sqrt{10} + 3)(\sqrt{10} - 3)\) is an integer.
True
False
9. Expanding \((4 - \sqrt{2})(4 + \sqrt{2})\) results in \(16 - 2\sqrt{2}\).
True
False
10. Expand and simplify: \((3\sqrt{5} - \sqrt{10})(2\sqrt{5} + \sqrt{2})\)
11. Given that \(x = 1 + \sqrt{2}\), find the value of \(x^2 - 2x + 1\).