d: \(\left(3\sqrt3+1\right)\left(2-\sqrt3\right)\)
\(=6\sqrt3-9+2-\sqrt3=5\sqrt3-7\)
e: \(\left(\sqrt5+2\sqrt2\right)\left(\sqrt5-2\sqrt2\right)=\left(\sqrt5\right)^2-8=5-8=-3\)
f: \(\left(\sqrt3+\sqrt5\right)\left(\sqrt3-\sqrt5\right)=3-5=-2\)
n: \(\left(\sqrt{75}+\sqrt{243}-\sqrt{48}\right):\sqrt3\)
\(=\left(5\sqrt3+9\sqrt3-4\sqrt3\right):\sqrt3\)
\(=\frac{10\sqrt3}{\sqrt3}=10\)
i: \(\left(2\sqrt{18}-3\sqrt{32}+6\sqrt2\right):\sqrt2\)
\(=\left(2\cdot3\sqrt2-3\cdot4\sqrt2+6\sqrt2\right):\sqrt2=0\)
j: \(\left(\sqrt2+1\right)^2+\left(\sqrt2-1\right)^2\)
\(=3+2\sqrt2+3-2\sqrt2\)
=3+3
=6
q: \(\left(\sqrt{27}-3\sqrt{32}+2\sqrt6\right):3\sqrt3\)
\(=\left(3\sqrt3-3\cdot4\sqrt2+2\sqrt6\right):3\sqrt3\)
\(=1-\frac{12\sqrt2}{3\sqrt3}+\frac{2\sqrt6}{3\sqrt3}=1-4\sqrt{\frac23}+\frac23\sqrt2\)
y: \(\left(\sqrt5-2\right)\left(3+\sqrt5\right)\) -2
\(=3\sqrt5+5-6-2\sqrt5-2=-3+\sqrt5\)
w: \(\left(\sqrt{28}-2\sqrt3+\sqrt7\right)\cdot\sqrt7+\sqrt{84}\)
\(=\left(2\sqrt7+\sqrt7-2\sqrt3\right)\cdot\sqrt7+2\sqrt{21}=21-2\sqrt{21}+2\sqrt{21}\)
=21
p: \(\left(3-\sqrt2\right)\left(5+\sqrt2\right)=15+3\sqrt2-5\sqrt2-2=13-2\sqrt2\)
r: \(\left(\sqrt3+1\right)^2+\left(1-\sqrt3\right)^2=4+2\sqrt3+4-2\sqrt3=8\)
o: \(\left(6-\sqrt7\right)\left(2\sqrt7-3\right)+\sqrt7\left(\sqrt2-5\right)\)
\(=12\sqrt7-18-14+3\sqrt7+\sqrt{14}-5\sqrt7=\sqrt{14}+10\sqrt7-32\)
t: \(\left(\sqrt{18}-\sqrt8\right):\sqrt2=\left(3\sqrt2-2\sqrt2\right):\sqrt2=\sqrt2:\sqrt2=1\)
z: \(\sqrt3\left(\sqrt3-1\right)-\left(\sqrt3-2\right)^2\)
\(=3-\sqrt3-\left(7-4\sqrt3\right)\)
\(=3-\sqrt3-7+4\sqrt3=-4+3\sqrt3\)
