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a: \(=10\sqrt{2}-4\sqrt{2}+6\sqrt{2}=12\sqrt{2}\)
b: \(=5\sqrt{7}-4\sqrt{7}+3\sqrt{7}=4\sqrt{7}\)
c: \(=\dfrac{3}{2}\sqrt{6}+\dfrac{2}{3}\sqrt{6}-2\sqrt{6}=\dfrac{1}{6}\sqrt{6}\)
d: \(=8\sqrt{5}-15\sqrt{5}+15\sqrt{5}-3\sqrt{5}=5\sqrt{5}\)
e: \(=\sqrt{5}+\dfrac{2}{5}\sqrt{5}+\sqrt{5}=2.4\sqrt{5}\)
f: \(=\dfrac{1}{5}\sqrt{5}+\dfrac{3}{2}\sqrt{2}+\dfrac{5}{2}\sqrt{2}=\dfrac{1}{5}\sqrt{5}+4\sqrt{2}\)
a) \(=\sqrt{\frac{9}{2}}-\sqrt{16.2}+\sqrt{36.2}-\sqrt{81.2}\)
\(=\frac{3}{2}\sqrt{2}-4\sqrt{2}+6\sqrt{2}-9\sqrt{2}\)
\(=\left(\frac{3}{2}-4+6-9\right)\sqrt{2}=\frac{-11}{2}\sqrt{2}\)
b) \(=\frac{\sqrt{5}+3-\sqrt{5}+3}{\left(\sqrt{5}-3\right)\left(\sqrt{5}+3\right)}.\frac{\sqrt{3}\left(\sqrt{3}-1\right)}{1-\sqrt{3}}\)
\(=\frac{6}{5-9}.\left(-\sqrt{3}\right)=\frac{3}{2}\sqrt{3}\)
c) \(=\left(\frac{a-1-4\sqrt{a}+\sqrt{a}+1}{a-1}\right):\frac{\sqrt{a}\left(\sqrt{a}-2\right)}{a-1}\)
\(=\frac{a-3\sqrt{a}}{a-1}.\frac{a-1}{\sqrt{a}\left(\sqrt{a}-2\right)}\)
\(=\frac{\sqrt{a}\left(\sqrt{a}-3\right)}{\sqrt{a}\left(\sqrt{a}-2\right)}=\frac{\sqrt{a}-3}{\sqrt{a}-2}\)
a)\(2\sqrt{18}+3\sqrt{8}-3\sqrt{32}-\sqrt{50}\)
\(=2\sqrt{9.2}+3\sqrt{4.2}-3\sqrt{16.2}-\sqrt{25.2}\)
\(=6\sqrt{2}+6\sqrt{2}-12\sqrt{2}-5\sqrt{2}\)
\(=-5\sqrt{2}\)
b) \(\sqrt{200}-\sqrt{32}-\sqrt{72}\)
\(=\sqrt{100.2}-\sqrt{16.2}-\sqrt{36.2}\)
\(=10\sqrt{2}-4\sqrt{2}-6\sqrt{2}\)
\(=0\)
c) \(\sqrt{175}-\sqrt{112}+\sqrt{63}\)
\(=\sqrt{25.7}-\sqrt{16.7}+\sqrt{9.7}\)
\(=5\sqrt{7}-4\sqrt{7}+3\sqrt{7}\)
\(=4\sqrt{7}\)
d) \(3\sqrt{8}-\sqrt{32}+4\sqrt{2}+\sqrt{162}\)
\(=3\sqrt{4.2}-\sqrt{16.2}+4\sqrt{2}+\sqrt{81.2}\)
\(=6\sqrt{2}-4\sqrt{2}+4\sqrt{2}+9\sqrt{2}\)
\(=15\sqrt{2}\)
3: \(\sqrt{12-3\sqrt{7}}-\sqrt{12-3\sqrt{7}}=0\)
4: \(\sqrt{7-2\sqrt{10}}-\sqrt{7+2\sqrt{10}}\)
\(=\sqrt{5}-\sqrt{2}-\sqrt{5}-\sqrt{2}\)
\(=-2\sqrt{2}\)
6: \(3\sqrt{3}+4\sqrt{12}-5\sqrt{27}\)
\(=3\sqrt{3}+8\sqrt{3}-15\sqrt{3}\)
\(=-4\sqrt{3}\)
\(\sqrt{162+72\sqrt{2}}=\sqrt{162+2\sqrt{36^2.2}}=\sqrt{144+2\sqrt{144.18}+18}\)
\(=\sqrt{\left(\sqrt{144}+\sqrt{18}\right)^2}=\sqrt{144}+\sqrt{18}=12+3\sqrt{2}\)
tick nha
\(a.\sqrt{200}-\sqrt{32}+\sqrt{72}=10\sqrt{2}-4\sqrt{2}+6\sqrt{2}=12\sqrt{2}\)
\(b.\sqrt{175}-\sqrt{112}+\sqrt{63}=5\sqrt{7}-4\sqrt{7}+3\sqrt{7}=4\sqrt{7}\)
\(c.4\sqrt{20}-3\sqrt{125}+5\sqrt{45}-15\sqrt{\dfrac{1}{5}}=8\sqrt{5}-15\sqrt{5}+15\sqrt{5}-3\sqrt{5}=5\sqrt{5}\)
\(\sqrt{2\cdot36}+\sqrt{2\cdot\dfrac{9}{4}}-\sqrt{2\cdot16}-\sqrt{2\cdot81}=6\sqrt{2}+\dfrac{3}{2}\sqrt{2}-4\sqrt{2}-9\sqrt{2}=\dfrac{-11}{2}\sqrt{2}\)