Simplify the following surds. 2. Rationalize these surds.

$$\sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2}$$ $$\sqrt{32} = \sqrt{16 \times 2} = 4\sqrt{2}$$

$$2\sqrt{2} + 4\sqrt{2} = (2+4)\sqrt{2} = 6\sqrt{2}$$

The final answer is $\boxed{6\sqrt{2}}$.

$$\sqrt{75} = \sqrt{25 \times 3} = 5\sqrt{3}$$ $$\sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2}$$

Since the radicals are different ($\sqrt{3}$ and $\sqrt{2}$), they cannot be combined further.

$$5\sqrt{3} - 3\sqrt{2}$$

The final answer is $\boxed{5\sqrt{3} - 3\sqrt{2}}$.

$$\sqrt{125} = \sqrt{25 \times 5} = 5\sqrt{5}$$ $$\sqrt{80} = \sqrt{16 \times 5} = 4\sqrt{5}$$

$$(15-8)\sqrt{5} = 7\sqrt{5}$$

The final answer is $\boxed{7\sqrt{5}}$.

$$\sqrt{x^3} = \sqrt{x^2 \times x} = x\sqrt{x}$$ $$\sqrt{x}$$ $$\sqrt{4x} = \sqrt{4 \times x} = 2\sqrt{x}$$

$$(x+1-2)\sqrt{x} = (x-1)\sqrt{x}$$

The final answer is $\boxed{(x-1)\sqrt{x}}$.

$$(14+2)\sqrt{6} - 4\sqrt{5} = 16\sqrt{6} - 4\sqrt{5}$$

The final answer is $\boxed{16\sqrt{6} - 4\sqrt{5}}$.

2. Rationalize these surds

A) $\frac{4}{\sqrt{5}}$

$$\frac{4\sqrt{5}}{5}$$

The final answer is $\boxed{\frac{4\sqrt{5}}{5}}$.

B) $\frac{7}{\sqrt{7}}$

$$\frac{7\sqrt{7}}{7} = \sqrt{7}$$

The final answer is $\boxed{\sqrt{7}}$.