1.
b, \(\sqrt{67+16\sqrt{3}}-\sqrt{21-12\sqrt{3}}\)
\(=\sqrt{\left(\sqrt{3}+8\right)^2}-\sqrt{\left(2\sqrt{3}-3\right)^2}\)
\(=\sqrt{3}+8-2\sqrt{3}+3\)
\(=11-\sqrt{3}\)
1.
a, \(\sqrt{21+4\sqrt{5}}+\sqrt{\left(1-\sqrt{5}\right)^2}\)
\(=\sqrt{\left(2\sqrt{5}+1\right)^2}+\sqrt{\left(1-\sqrt{5}\right)^2}\)
\(=2\sqrt{5}+1+\sqrt{5}-1\)
\(=3\sqrt{5}\)
2.
a, \(3\sqrt{50}-0,4\sqrt{200}+\dfrac{2}{3}\sqrt{18}\)
\(=3.5\sqrt{2}-\dfrac{2}{5}.10\sqrt{2}+\dfrac{2}{3}.9\sqrt{2}\)
\(=17\sqrt{2}\)
2.
b, \(6\sqrt{75}-\dfrac{1}{3}\sqrt{405}-\sqrt{108}+5\sqrt{20}\)
\(=6.5\sqrt{3}-\dfrac{1}{3}.9\sqrt{5}-6\sqrt{3}+5.2\sqrt{5}\)
\(=24\sqrt{3}+7\sqrt{5}\)
2.
c, \(5\sqrt{\dfrac{1}{5}}-\sqrt{45}-\dfrac{1}{2}\sqrt{180}+\dfrac{4}{3}\sqrt{405}\)
\(=\sqrt{5}-3\sqrt{5}-3\sqrt{5}+12\sqrt{5}\)
\(=7\sqrt{5}\)
2.
d, \(2\sqrt{27}-12\sqrt{\dfrac{1}{3}}+\sqrt{75}-4\sqrt{12}\)
\(=6\sqrt{3}-4\sqrt{3}+5\sqrt{3}-8\sqrt{3}\)
\(=-\sqrt{3}\)
