Đáp án:
Giải thích các bước giải:
$a) 2\sqrt{3}+\sqrt{(2-\sqrt{3})^2}=2\sqrt{3}+2-\sqrt{3}=2+\sqrt{3}\\
b) \frac{5+\sqrt{5}}{5-\sqrt{5}}+\frac{5-\sqrt{5}}{5+\sqrt{5}}=\frac{(5+\sqrt{5})^2+(5-\sqrt{5})^2}{(5-\sqrt{5})(5+\sqrt{5})}=\frac{25+10\sqrt{5}+5+25-10\sqrt{5}+5}{5^2-5}=\frac{60}{20}=3\\
c) (\sqrt{28}-\sqrt{12}-\sqrt{7}).\sqrt{7}+2\sqrt{21}=(2\sqrt{7}-2\sqrt{3}-\sqrt{7}).\sqrt{7}+2\sqrt{21}=14-2\sqrt{21}-7+2\sqrt{21}=7\\
d) \sqrt{17-3\sqrt{32}}+ \sqrt{17+3\sqrt{32}}= \sqrt{17-12\sqrt{2}}+ \sqrt{17+12\sqrt{2}}=\sqrt{(2\sqrt{2})^2-2.2\sqrt{2}.3+3^2}+\sqrt{(2\sqrt{2})^2+2.2\sqrt{2}.3+3^2}=\sqrt{(2\sqrt{2}-3)^2}+\sqrt{(2\sqrt{2}+3)^2}=2\sqrt{2}-3+2\sqrt{2}+3=4\sqrt{2}\\
e)(2+\sqrt{5}+\sqrt{3})(2+\sqrt{5}-\sqrt{3})=(2+\sqrt{5})^2-3=4+2\sqrt{5}+5-3=6+2\sqrt{5}\\
f) (\sqrt{\frac{1}{3}}-\sqrt{\frac{4}{3}}+\sqrt{3}):\sqrt{3}=(\frac{\sqrt{3}}{3}-\frac{2\sqrt{3}}{3}+\sqrt{3}):\sqrt{3}=\frac{1}{3}-\frac{2}{3}+1=\frac{2}{3}$
