Expanding Brackets with Surds

Expanding Brackets with Surds

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 \( (\sqrt{7} + 1)(\sqrt{7} - 1) \)?

8. Expand and simplify: \( (3\sqrt{2} - \sqrt{5})^2 \)

9. Expand and simplify: \( (\sqrt{x} + \sqrt{y})(\sqrt{x} - \sqrt{y}) \)