1)3√3+√9-√162 2)4√5)+√3)² 3-2√2/1+√2

$$\sqrt{9} = 3$$ $$\sqrt{162} = \sqrt{81 \times 2} = \sqrt{81} \times \sqrt{2} = 9\sqrt{2}$$

$$3\sqrt{3} + 3 - 9\sqrt{2}$$

The terms are not like terms, so they cannot be combined further.

The final answer is $\boxed{3\sqrt{3} + 3 - 9\sqrt{2}}$.

:

$$(4\sqrt{5}+\sqrt{3})^2$$

Here, $a = 4\sqrt{5}$ and $b = \sqrt{3}$.

$$(4\sqrt{5})^2 + 2(4\sqrt{5})(\sqrt{3}) + (\sqrt{3})^2$$

$$(4\sqrt{5})^2 = 4^2 \times (\sqrt{5})^2 = 16 \times 5 = 80$$ $$2(4\sqrt{5})(\sqrt{3}) = 8\sqrt{5 \times 3} = 8\sqrt{15}$$ $$(\sqrt{3})^2 = 3$$

$$80 + 8\sqrt{15} + 3$$ $$83 + 8\sqrt{15}$$

The final answer is $\boxed{83 + 8\sqrt{15}}$.

:

$$\frac{3-2\sqrt{2}}{1+\sqrt{2}}$$

The conjugate of $1+\sqrt{2}$ is $1-\sqrt{2}$.

$$\frac{3-2\sqrt{2}}{1+\sqrt{2}} \times \frac{1-\sqrt{2}}{1-\sqrt{2}}$$

Numerator:

$$(3-2\sqrt{2})(1-\sqrt{2}) = 3(1) + 3(-\sqrt{2}) - 2\sqrt{2}(1) - 2\sqrt{2}(-\sqrt{2})$$ $$= 3 - 3\sqrt{2} - 2\sqrt{2} + 2(\sqrt{2})^2$$ $$= 3 - 5\sqrt{2} + 2(2)$$ $$= 3 - 5\sqrt{2} + 4$$ $$= 7 - 5\sqrt{2}$$

Denominator:

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

$$-(7 - 5\sqrt{2}) = -7 + 5\sqrt{2}$$

The final answer is $\boxed{-7 + 5\sqrt{2}}$.