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, $(\sqrt{5}+2\sqrt{2})(\sqrt{5}-2\sqrt{2})$

$=(\sqrt{5})^2-(2\sqrt{2})^2$

$=5-8$

$=-3$

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