$\text{a)}\underset{<0}{\underbrace{\left|1-\sqrt{3}\right|}}+\underset{<0}{\underbrace{\left|\sqrt{3}-2\right|}}=-1+\sqrt{3}-\sqrt{3}+2=1$       

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$\text{b)}2\underset{<0}{\underbrace{\left|-3-\sqrt{5}\right|}}-\underset{=\sqrt{16}-\sqrt{20}<0}{\underbrace{\left|4-2\sqrt{5}\right|}}=2\left(3+\sqrt{5}\right)-\left(-4+2\sqrt{5}\right)=$  

$=6+2\sqrt{5}+4-2\sqrt{5}=10$  

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$\text{c)}2\underset{<0}{\underbrace{\left|3-\pi \right|}}-\underset{>0}{\underbrace{\left|2\pi -5\right|}}=2\left(-3+\pi \right)-\left(2\pi -5\right)=-6+2\pi -2\pi +5=-1$  

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$\text{d)}3\underset{=\sqrt{7}-\sqrt{8}<0}{\underbrace{\left|\sqrt{7}-2\sqrt{2}\right|}}-\underset{=\sqrt{72}-\sqrt{63}>0}{\underbrace{\left|6\sqrt{2}-3\sqrt{7}\right|}}=3\left(-\sqrt{7}+2\sqrt{2}\right)-\left(6\sqrt{2}-3\sqrt{7}\right)=$  

$=-3\sqrt{7}+6\sqrt{2}-6\sqrt{2}+3\sqrt{7}=0$  

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$\text{e)}4-2\underset{=\sqrt{18}-\sqrt{27}<0}{\underbrace{\left|\sqrt{18}-3\sqrt{3}\right|}}+\underset{=\sqrt{16}-\sqrt{18}<0}{\underbrace{\left|4-3\sqrt{2}\right|}}=4-2\left(-\sqrt{18}+3\sqrt{3}\right)+\left(-4+3\sqrt{2}\right)=$  

$=4+2\sqrt{18}-6\sqrt{3}-4+3\sqrt{2}=2\cdot 3\sqrt{2}-6\sqrt{3}+3\sqrt{2}=$  

$=6\sqrt{2}-6\sqrt{3}+3\sqrt{2}=9\sqrt{2}-6\sqrt{3}$  

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$\text{f)}\sqrt{150}-\underset{=\sqrt{12}-\sqrt{24}<0}{\underbrace{\left|2\sqrt{3}-\sqrt{8}\cdot \sqrt{3}\right|}}-7\underset{=\sqrt{6}-\sqrt{4}>0}{\underbrace{\left|\sqrt{6}-2\right|}}=\sqrt{25\cdot 6}-\left(-2\sqrt{3}+2\sqrt{2}\cdot \sqrt{3}\right)-7\left(\sqrt{6}-2\right)=$  

$=5\sqrt{6}+2\sqrt{3}-2\sqrt{6}-7\sqrt{6}+14=2\sqrt{3}-4\sqrt{6}+14$