1. Simplify \(\sqrt{98}\): \(\sqrt{98} = \sqrt{49 \times 2} = \sqrt{49} \times \sqrt{2} = 7\sqrt{2}\). 2. Rationalize the denominator of \(\frac{3}{\sqrt{5} - 2}\): Multiply numerator and denominator by the conjugate \(\sqrt{5} + 2\): \[\frac{3}{\sqrt{5} - 2} \times \frac{\sqrt{5} + 2}{\sqrt{5} + 2} = \frac{3(\sqrt{5} + 2)}{(\sqrt{5})^2 - 2^2} = \frac{3(\sqrt{5} + 2)}{5 - 4} = 3(\sqrt{5} + 2) = 3\sqrt{5} + 6\]. 3. Simplify \(\sqrt{300} + \sqrt{48}\): \(\sqrt{300} = \sqrt{100 \times 3} = 10\sqrt{3}\), \(\sqrt{48} = \sqrt{16 \times 3} = 4\sqrt{3}\), So \(\sqrt{300} + \sqrt{48} = 10\sqrt{3} + 4\sqrt{3} = 14\sqrt{3}\). 4a. Simplify \(22\sqrt{35} + 11\sqrt{5}\): Here, the terms are not like terms because \(\sqrt{35} \neq \sqrt{5}\), so expression stays: \(22\sqrt{35} + 11\sqrt{5}\). 4b. Simplify \(\sqrt{2} \times \sqrt{10}\): \(\sqrt{2} \times \sqrt{10} = \sqrt{2 \times 10} = \sqrt{20} = \sqrt{4 \times 5} = 2\sqrt{5}\). 5. Expand and simplify \(2\sqrt{3}(2\sqrt{30} - 4\sqrt{3})\): \(2\sqrt{3} \times 2\sqrt{30} = 4\sqrt{3 \times 30} = 4\sqrt{90} = 4 \times 3\sqrt{10} = 12\sqrt{10}\), \(2\sqrt{3} \times (-4\sqrt{3}) = -8\sqrt{9} = -8 \times 3 = -24\), So combined: \(12\sqrt{10} - 24\). Final answers: 1. \(7\sqrt{2}\) 2. \(3\sqrt{5} + 6\) 3. \(14\sqrt{3}\) 4a. \(22\sqrt{35} + 11\sqrt{5}\) 4b. \(2\sqrt{5}\) 5. \(12\sqrt{10} - 24\)