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\(\sqrt{12}+2\sqrt{27}+3\sqrt{75}-9\sqrt{48}\)
\(=2\sqrt{3}+6\sqrt{3}+15\sqrt{3}-36\sqrt{3}\)
\(=-13\sqrt{3}\)
\(\sqrt{27}:\sqrt{3}-\sqrt{48}+2\sqrt{12}=\sqrt{3^2.3}:\sqrt{3}-\sqrt{4^2.3}+2\sqrt{2^2.3}\)
\(=3\sqrt{3}:\sqrt{3}-4\sqrt{3}+4\sqrt{3}=3\sqrt{3}:\sqrt{3}=3\)
= ( 7\(\sqrt{16\cdot3}\)+3\(\sqrt{9\cdot3}\)-3\(\sqrt{4\cdot3}\)) /\(\sqrt{3}\)
=(49\(\sqrt{3}\)+ 9\(\sqrt{3}\)-6 \(\sqrt{3}\)) /\(\sqrt{3}\)
=52
\(\left(\sqrt{27}-3\sqrt{2}+2\sqrt{6}\right):3\sqrt{3}\)
\(=\left(3\sqrt{3}-3\sqrt{2}+2\sqrt{6}\right):3\sqrt{3}\)
Bài làm:
\(\sqrt{14-8\sqrt{3}}-\sqrt{24-12\sqrt{3}}\)
\(=\sqrt{8-8\sqrt{3}+6}-\sqrt{18-12\sqrt{3}+6}\)
\(=\sqrt{\left(2\sqrt{2}-\sqrt{6}\right)^2}-\sqrt{\left(3\sqrt{2}-\sqrt{6}\right)^2}\)
\(=2\sqrt{2}-\sqrt{6}-3\sqrt{2}+\sqrt{6}\)
\(=-\sqrt{2}\)
Học tốt
\(=\sqrt{5}-\sqrt{3-\sqrt{20-2.2\sqrt{5}.3}+9}=\sqrt{5}-\sqrt{3-\sqrt{\left(2\sqrt{5}-3\right)^2}}=\)
\(\sqrt{5}-\sqrt{6-2\sqrt{5}}=\sqrt{5}-\sqrt{\left(\sqrt{5}-1\right)^2}=\sqrt{5}-\sqrt{5}+1=1.\)
\(=\left(2\sqrt{3}+\sqrt{3}\right)\left(3\sqrt{3}-\sqrt{3}\right)=3\sqrt{3}\cdot2\sqrt{3}=18\)
\(=\left(\sqrt{12}.\sqrt{27}\right)-\left(\sqrt{12}.\sqrt{3}\right)+\left(\sqrt{3}.\sqrt{27}\right)-\left(\sqrt{3}.\sqrt{3}\right)\)
\(=18-6+9-9\)
\(=12\)