Simplify radical expressions: 2crypt63 - 4crypt28 + 5crypt112

Step 1: Simplify each radical term by factoring out perfect squares.

: $2\sqrt{63} - 4\sqrt{28} + 5\sqrt{112}$

$$2\sqrt{9 \times 7} - 4\sqrt{4 \times 7} + 5\sqrt{16 \times 7}$$ $$2 \times 3\sqrt{7} - 4 \times 2\sqrt{7} + 5 \times 4\sqrt{7}$$ $$6\sqrt{7} - 8\sqrt{7} + 20\sqrt{7}$$

Combine the terms:

$$(6 - 8 + 20)\sqrt{7}$$ $$18\sqrt{7}$$

The simplified expression is $\boxed{18\sqrt{7}}$.

: $\sqrt{27} - \sqrt{18} - 2\sqrt{8} + \sqrt{12}$

$$\sqrt{9 \times 3} - \sqrt{9 \times 2} - 2\sqrt{4 \times 2} + \sqrt{4 \times 3}$$ $$3\sqrt{3} - 3\sqrt{2} - 2 \times 2\sqrt{2} + 2\sqrt{3}$$ $$3\sqrt{3} - 3\sqrt{2} - 4\sqrt{2} + 2\sqrt{3}$$

Combine like terms:

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

The simplified expression is $\boxed{5\sqrt{3} - 7\sqrt{2}}$.

: $\sqrt{75} - 3\sqrt{48} + \sqrt{45} - 2\sqrt{12}$

$$\sqrt{25 \times 3} - 3\sqrt{16 \times 3} + \sqrt{9 \times 5} - 2\sqrt{4 \times 3}$$ $$5\sqrt{3} - 3 \times 4\sqrt{3} + 3\sqrt{5} - 2 \times 2\sqrt{3}$$ $$5\sqrt{3} - 12\sqrt{3} + 3\sqrt{5} - 4\sqrt{3}$$

Combine like terms:

$$(5 - 12 - 4)\sqrt{3} + 3\sqrt{5}$$ $$-11\sqrt{3} + 3\sqrt{5}$$

The simplified expression is $\boxed{-11\sqrt{3} + 3\sqrt{5}}$.

: $4\sqrt{32} - 3\sqrt{50} - 4\sqrt{18} + 5\sqrt{108}$

$$4\sqrt{16 \times 2} - 3\sqrt{25 \times 2} - 4\sqrt{9 \times 2} + 5\sqrt{36 \times 3}$$ $$4 \times 4\sqrt{2} - 3 \times 5\sqrt{2} - 4 \times 3\sqrt{2} + 5 \times 6\sqrt{3}$$ $$16\sqrt{2} - 15\sqrt{2} - 12\sqrt{2} + 30\sqrt{3}$$

Combine like terms:

$$(16 - 15 - 12)\sqrt{2} + 30\sqrt{3}$$ $$-11\sqrt{2} + 30\sqrt{3}$$

The simplified expression is $\boxed{-11\sqrt{2} + 30\sqrt{3}}$.

: $3\sqrt{48} + \sqrt{192} + 3\sqrt{12} - \sqrt{147}$

$$3\sqrt{16 \times 3} + \sqrt{64 \times 3} + 3\sqrt{4 \times 3} - \sqrt{49 \times 3}$$ $$3 \times 4\sqrt{3} + 8\sqrt{3} + 3 \times 2\sqrt{3} - 7\sqrt{3}$$ $$12\sqrt{3} + 8\sqrt{3} + 6\sqrt{3} - 7\sqrt{3}$$

Combine like terms:

$$(12 + 8 + 6 - 7)\sqrt{3}$$ $$19\sqrt{3}$$

The simplified expression is $\boxed{19\sqrt{3}}$.

: $3\sqrt{48} - \sqrt{75} + 2\sqrt{27}$

$$3\sqrt{16 \times 3} - \sqrt{25 \times 3} + 2\sqrt{9 \times 3}$$ $$3 \times 4\sqrt{3} - 5\sqrt{3} + 2 \times 3\sqrt{3}$$ $$12\sqrt{3} - 5\sqrt{3} + 6\sqrt{3}$$

Combine like terms:

$$(12 - 5 + 6)\sqrt{3}$$ $$13\sqrt{3}$$

The simplified expression is $\boxed{13\sqrt{3}}$.

: $\sqrt{128} - 2\sqrt{72} + \sqrt{32} + \sqrt{8}$

$$\sqrt{64 \times 2} - 2\sqrt{36 \times 2} + \sqrt{16 \times 2} + \sqrt{4 \times 2}$$ $$8\sqrt{2} - 2 \times 6\sqrt{2} + 4\sqrt{2} + 2\sqrt{2}$$ $$8\sqrt{2} - 12\sqrt{2} + 4\sqrt{2} + 2\sqrt{2}$$

Combine like terms:

$$(8 - 12 + 4 + 2)\sqrt{2}$$ $$2\sqrt{2}$$

The simplified expression is $\boxed{2\sqrt{2}}$.