Surds - Simplifying Surds

Simplify each of the following surds without using a calculator.

1. \(\frac{\sqrt{75}\times \sqrt{72}}{\sqrt{24}}\)
2. \(\frac{4}{5\sqrt{2}}\)
3. \(\sqrt{32}+\sqrt{50}\)
4. \(\left( 7+2\sqrt{3} \right)\left( 5-\sqrt{3} \right)\)