a: \(3\sqrt{27}-\sqrt{108}+2\sqrt{180}-3\sqrt{80}\)
\(=3\cdot3\sqrt3-6\sqrt3+2\cdot6\sqrt5-3\cdot4\sqrt5\)
\(=9\sqrt3-6\sqrt3+12\sqrt5-12\sqrt5=3\sqrt3\)
b: \(2\sqrt{16}-3\cdot\sqrt{25}+4\cdot\sqrt{\left(-7\right)^2}\)
\(=2\cdot4-3\cdot5+4\cdot7\)
=8-15+28
=-7+28
=21
c: \(\sqrt{\left(\sqrt3-2\right)^2}+\sqrt{\left(\sqrt3-1\right)^2}\)
\(=2-\sqrt3+\sqrt3-1\)
=2-1
=1
d: \(\sqrt{6-2\sqrt5}-\sqrt5\)
\(=\sqrt{\left(\sqrt5-1\right)^2}-\sqrt5\)
\(=\sqrt5-1-\sqrt5=-1\)
e: \(\sqrt2-\sqrt{6-\sqrt{32}}\)
\(=\sqrt2-\sqrt{6-4\sqrt2}\)
\(=\sqrt2-\sqrt{\left(2-\sqrt2\right)^2}=\sqrt2-2+\sqrt2=2\sqrt2-2\)
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