Expanding Brackets with Surds

Expanding Brackets with Surds

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. Expand and simplify: \((2\sqrt{3} + 1)(3\sqrt{3} - 2)\)

9. Expand and simplify: \((4 - \sqrt{x})(4 + \sqrt{x})\)