Rationalising a two term denominator

12 questions

1. Expand the following expression: (3\sqrt {2} + \sqrt {3})(3\sqrt {2} - \sqrt {3})
2. Expand the following expression: (\sqrt {6} + 1)(\sqrt {6} - 1)
3. Expand the following expression: (2\sqrt {5} - 3\sqrt {3})(2\sqrt {5} + 3\sqrt {3})
4. Expand the following expression: (5\sqrt {7} - 4\sqrt {2})(5\sqrt {7} + 4\sqrt {2})
5. Expand the following expression: (\sqrt {8} + \sqrt {2})(\sqrt {2} - \sqrt {8})
6. Expand the following expression: (\sqrt {10} + 2\sqrt {5})(2\sqrt {5} - \sqrt {10})
7. Match the brackets and their expanded form.
8. You can use the ___ to make an integer from a surd expression.
9. What would you multiply (13 + \sqrt {17}) by to make an integer?
10. Simplify {{8} \over {4 - \sqrt {5}}}
11. Express {6} \over {2\sqrt {3} - 4} in the form a(d+\sqrt {3}). What is the value of a?
12. Express {6} \over {2\sqrt {3} - 4} in the form a(d+\sqrt {3}). What is the value of d?

License: OGL