Bài tập 3:
a, $\sqrt{3}.\sqrt{27}$
$=\sqrt{3}.3\sqrt{3}$
$=3.3$
$=9$
b, $\sqrt{7}.\sqrt{63}$
$=\sqrt{7}.3\sqrt{7}$
$=7.3$
$=21$
c, $(2+\sqrt{3})(2-\sqrt{3})$
$=2^2-(\sqrt{3})^2$
$=4-3$
$=1$
d, $\sqrt{2}.\sqrt{8}$
$=\sqrt{2.8}$
$=\sqrt{16}$
$=4$
e, $2\sqrt{3}(2\sqrt{6}-\sqrt{3}+1)$
$=2\sqrt{3}.2\sqrt{6}-2\sqrt{3}.\sqrt{3}+2\sqrt{3}$
$=4\sqrt{18}-2.3+2\sqrt{3}$
$=12\sqrt{2}-6+2\sqrt{3}$
f, $(5+2\sqrt{6})(5-2\sqrt{6})$
$=5^2-(2\sqrt{6})^2$
$=25-4.6$
$=25-24$
$=1$
g, $\sqrt{\sqrt{10}+1}.\sqrt{\sqrt{10}-1}$
$=\sqrt{(\sqrt{10}+1)(\sqrt{10}-1)}$
$=\sqrt{10-1}$
$=\sqrt{9}$
$=3$
h, $(\sqrt{3}+\sqrt{2})(\sqrt{3}-\sqrt{2})$
$=3-2$
$=1$
i, $(\sqrt{3}+\sqrt{5})(\sqrt{3}-\sqrt{5})$
$=3-5$
$=-2$
Bài tập 5:
a, $(3\sqrt{2}+2\sqrt{3})^2$
$=(3\sqrt{2})^2+2.3\sqrt{2}.2\sqrt{3}+(2\sqrt{3})^2$
$=18+12\sqrt{6}+12$
$=30+12\sqrt{6}$
b, $(3\sqrt{2}-2\sqrt{3})^2$
$=(3\sqrt{2})^2-2.3\sqrt{2}.2\sqrt{3}+(2\sqrt{3})^2$
$=18-12\sqrt{6}+12$
$=30-12\sqrt{6}$
c, $(3\sqrt{2}+2\sqrt{3})(3\sqrt{2}-2\sqrt{3})$
$=(3\sqrt{2})^2-(2\sqrt{3})^2$
$=18-12$
$=6$
d, $(\sqrt{5}+2\sqrt{2})^2$
$=(\sqrt{5})^2+2.\sqrt{5}.2\sqrt{2}+(2\sqrt{2})^2$
$=5+4\sqrt{10}+8$
$=13+4\sqrt{10}$
e, $(\sqrt{5}-2\sqrt{2})^2$
$=(\sqrt{5})^2-2.\sqrt{5}.2\sqrt{2}+(2\sqrt{2})^2$
$=5-4\sqrt{10}+8$
$=13-4\sqrt{10}$
f, $(\sqrt{5}+2\sqrt{2})(\sqrt{5}-2\sqrt{2})$
$=(\sqrt{5})^2-(2\sqrt{2})^2$
$=5-8$
$=-3$
