d: \(D=2\sqrt{12}-\sqrt{48}+3\cdot\sqrt{27}-\sqrt{108}\)
\(=2\cdot2\sqrt3-4\sqrt3+3\cdot3\sqrt3-6\sqrt3\)
\(=9\sqrt3-6\sqrt3=3\sqrt3\)
e: \(E=\left(2\cdot\sqrt{1\frac{9}{16}}-\sqrt{5\frac{1}{16}}\right):\sqrt{16}\)
\(=\left(2\cdot\sqrt{\frac{25}{16}}-\sqrt{\frac{81}{16}}\right):4=\left(2\cdot\frac54-\frac94\right):4\)
\(=\frac14:4=\frac{1}{16}\)
f: \(F=2\cdot\sqrt{\frac{16}{3}}-3\cdot\sqrt{\frac{1}{27}}-6\cdot\sqrt{\frac{4}{75}}\)
\(=2\cdot\frac{4}{\sqrt3}-3\cdot\frac{1}{3\sqrt3}-6\cdot\frac{2}{5\sqrt3}\)
\(=\frac{8}{\sqrt3}-\frac{1}{\sqrt3}-\frac{12}{5\sqrt3}=\frac{7}{\sqrt3}-\frac{12}{5\sqrt3}=\frac{35}{5\sqrt3}-\frac{12}{5\sqrt3}=\frac{23}{5\sqrt3}=\frac{23\sqrt3}{15}\)
a: \(A=\left(\sqrt{15}-2\sqrt3\right)^2+12\cdot\sqrt5\)
\(=15+12-2\cdot\sqrt{15}\cdot2\sqrt3+12\sqrt5\)
\(=27-4\cdot3\sqrt5+12\sqrt5\)
=27
b: \(B=3\sqrt{50}-7\sqrt8+12\sqrt{18}\)
\(=3\cdot5\sqrt2-7\cdot2\sqrt2+12\cdot3\sqrt2\)
\(=15\sqrt2-14\sqrt2+36\sqrt2=37\sqrt2\)
c: \(C=2\sqrt{80}-2\cdot\sqrt{245}+2\cdot\sqrt{180}\)
\(=2\cdot4\sqrt5-2\cdot7\sqrt5+2\cdot6\sqrt5\)
\(=8\sqrt5-14\sqrt5+12\sqrt5=6\sqrt5\)
